There are six stats, split into the categories ENTERIC, NOETIC, and SYNCRETIC.
ENTERIC
The enteric mind is a long, twisted, writhing thing composed of neurons, muscle, and bacterial colonies. Usually secondary to the cephalic mind, it began to take over the body upon the death of the brain.
Vigor Mortis - strength/constitution/will stat, as well as doing stuff related to being dead. Your corpse yearns for oblivion: high Vigor Mortis will make it hard to survive deadly wounds.
Somatics - proprioception, reflex, and muscle memory, as well as the physical component of magic. Magic is a two-way street: high Somatics will make magic effects more potent against you.
NOETIC
Before the start of the game, the soul was ripped from the underworld and fused to the body. You don’t know if it’s yours. Whether you like it or not, it’s time to get used to being a person again.
Memory - the soul’s connection to the dead brain in the body, as well as connection to the mind of its previously living self. Intelligence stat, used for research, lore, identification, and anything related to the previous life of the body or soul before it died. Mind control directly attacks the brain: high Memory will make you more vulnerable to it.
Sight - the soul’s connection to the external physical and spiritual worlds. A wisdom/intuition/perception stat, as well as the mental component of magic. Sometimes it’s better not knowing: high Sight will make it harder to avoid learning spells or forbidden knowledge.
SYNCRETIC
The paradox: If two are one, then there are three. You are an interference pattern, the self created by the self observing the self.
Poise - balance, restraint, agility, pretending to be a living person, finesse weapons and martial arts. The demise of cowards: high Poise will make you more vulnerable to poison and disease.
Thirst - the desire to remain alive, and to indulge in the pleasures of life. Used for stealing, survival, tracking, seduction, “fighting dirty” and anything related to food or beverage. Sometimes it’s just not appropriate: high Thirst will make it difficult to resist devouring any corpse you come across.

Character creation: Allocate 3 points among the 6 stats. You can make one skill a -1 to get 4 points instead.
Roll a random spell from a big table.

Stat improvement: If you eat the entrails of something you killed, the stat category which the creature had the most affinity for will be eligible for improvement during your next rest. Roll a d10 over one of the stats in that category to see if it increases by 1.
(“Eating the entrails” can mean many things. Eating the brains, hearts, guts, sucking the blood, inhaling the soul. Whatever is most appropriate for your character.)

Skills: Can be anything. d1->d2->d4->d6->d8->d10->d12. Upon resting, pick one eligible skill to increase by 1 step. A skill is eligible if, since the last rest, you rolled the highest possible number for the skill die but still failed the check. If no skills are eligible, pick a check you failed that you didn’t use a skill for, and gain a new d1 skill that would have been applicable.
If you roll a 1 on a skill die but still succeed the check, mark the skill to degrade. Each rest, a random marked skill degrades by 1 step and loses its mark. Only do this for skills d4 or greater.

Checks: D20+most appropriate stat+optional skill, roll over a target number. The skill used will color the nature of the resulting victory or failure. A skill deemed inappropriate will subtract from instead of adding to your roll.
Saves: D20+stat, roll UNDER a target number (usually 11). Basically a check you don’t want to succeed. (Failing a death save is “succeeding at dying.”) Saves make it risky to increase stats super high.
Vigor Mortis for death saves.
Somatics for magic saves.
Memory for saves against mind control/illusions.
Sight for saves against learning spells or other metaphysically dangerous knowledge.
Poise for saves against poison and disease.
Thirst for saves against being compelled to devour a corpse you see.
For other saves, choose whichever stat you deem to be most appropriate. Be consistent.

Combat and Wounds:
You can have 3 minor, 2 medium, 1 severe, X deadly wounds. Minor wounds have no effect. Medium wounds subtract 1 from all d20s for checks (not saves). A severe wound imposes disadvantage (roll 2 d20s for checks {not saves}, take the lower number).
Enemies still have HP, attacking them is a d20-style skill check to hit them with your attack, then little dice (around 1d8 but depends on the weapon) to determine damage.
Enemies roll little damage dice to attack (e.g. 2d8 or whatever their stat block says), that result creates the value the player must roll a d20 check over to avoid receiving wounds. Wound severity can either be specified on the monster’s statblock or rolled on a d6 (default is 1-3 minor, 4,5 medium, 6 severe, but feel free to adjust the table as appropriate to the situation).
If you are at capacity for a certain severity level of wound, bump any further ones of that level up one step. Whenever you receive a deadly wound, save vs death (default target 11). Every hour while you have deadly wounds, decrement the target by the number of deadly wounds you have and save again.
Resting with deadly wounds kills you with no save. (Unless you rest at a hospital, in which case 1 deadly wound is cleared right then, the second takes another day, the third takes a week, and the fourth results in death no matter what.) Otherwise, a rest clears your minor wounds and reduces the severity of one medium and one severe wound by 1 step.
Wounds have names, and may have additional effects (positive or negative) attached to them which linger until the wound is healed completely.

Spells: Everyone knows one random spell to start out with, it hitched a ride with your soul on the way from the underworld.
GLOG-style spellcasting: Roll from a pool of d6 magic dice to cast a spell. The more dice you roll, and the higher the total value, the more potent the spell’s effect. A good benchmark is a damage-dealing spell does [SUM] + [DICE] damage, or [SUM] damage plus an additional effect that scales with [DICE].
Dice that land on a 4, 5, or 6 are depleted and can’t be used for casting until the next rest. Each point of a spellcasting stat corresponds to a magic die, rolling in the upper half of it and depleting it actually lowers that skill by 1 until you rest. If your Somatics and Sight are both zero you can’t spellcast.
Healing spells are like inverse attacks. Whatever their result, roll a d20 under that number to completely remove a wound of your choice. (I guess… a “save vs. not receiving healing” …? Kind of bullshit… use Rigor Mortis to hinder the roll if you want to be really mean.)
When you roll doubles, the spell fails, and you suffer a mishap:
If both dice are Somatics dice, suffer a wound: minor if the matched number is a 1, 2, or 3, medium if it’s 4 or 5, severe if it’s 6.
If both dice are Sight dice, you can’t cast spells for the next N rests, where N is the matched number.
If the match is between a Somatics die and a Sight die, the spell casts normally, but with a random valid target/center. If the matched number is a 6, you’re the target/center. (If the spell has no target or center, cast it normally, but suffer both the Somatics and Sight mishaps for that number.)
Triples aren’t special, but they are very bad; there are three possible pairs formed between the three dice. Quadruples form six possible pairs. Do the math yourself for anything further.

Rests:
* Gain back all depleted spell stats.
* Remove all minor wounds, then one medium wound becomes minor and one severe wound becomes medium. (The wounds may or may not necessarily be healed in the fiction, but you as an undead creature have adjusted to them.)
* If you have a deadly wound, die.
* Improve one eligible skill, degrade one random marked skill.
* In each eligible stat category, you may roll to improve one of those stats.
* (skills and stats can’t be double-eligible, it’s just a boolean.)
* Clear all eligible skills and stats. (Skills marked for degradation stay marked until that actually happens.)
* Things that last until your next rest end.

First rest each day takes a combat turn (essentially free outside of combat).
Second takes ten minutes, and costs a snack.
Third takes an hour, costs a lunch, and you might get ambushed if you’re not somewhere safe.
Fourth takes until the next morning, costs a hearty dinner, and you might get ambushed, killed, and/or your shit stolen if you’re not somewhere safe.
The first, second, and third can actually be used in any order. The fourth always takes until the next day so there’s rarely going to be a reason to use it without having used the first three. Maybe you’re conserving food?

The Goal: Whoever or whatever resurrected you has placed a geas upon you. To be able to return peacefully to death, you must either fulfill the geas or kill the entity that did this to you.
Only by the above-mentioned paths may you find true rest. Dying from deadly wounds is not a good end. Your wretched body and soul will rise again, years, decades, or even centuries in the future, having lost all memory, subject to the geas all over again.
Resisting the geas is a save against mind control. A successful save lasts until midnight, a failure means the geas keeps hold of you at least until your next rest.
Members of the party may have the same geas, or be subjected to different ones. Undead creatures sometimes gravitate towards each other, forming communities, and can feel a great sense of kinship despite the great variations in their origins and natures. Many with relatively unobtrusive geases may try to live out their lives as normally as possible, but the toll inevitably will become unbearable.

Origins: Feel free to come up with your own, but here are a couple examples. The stat modifications are all -1 to one stat, +1 to another - this makes use of the character creation option to do just that. So, if you use one of these, that’s your one negative stat and fourth point allocation, don’t double dip.

VAMPIRE LORD. -1 Vigor Mortis, +1 Memory. Vampire lords usually give a geas along the lines of “eternal servitude to me.” Very restrictive, impossible to ever complete, but also he’s kind of just a guy (a very powerful one) who’s weak to like a million different things. (Sunlight, stakes, running water…) Vampire lords aren’t undead, they’re a type of living creature. Their blood-drinking thralls (that’s you!) are undead, though.

LICH KING. -1 Sight, +1 Thirst. The Lich King is a disgusting villain who lacks any sympathy for those suffering the same plight as him. He has decided to “delegate” his geas, subjecting countless souls to the hell of undeath and sending them out into the world to do his dirty work. Being undead, he can’t be truly killed unless his geas is fulfilled. On the plus side, though, the tasks he demands are usually straightforward, each being a simple step in his grander plan towards his own death.

UNFINISHED BUSINESS. -1 Poise, +1 Somatics. A rather spooky option with no concrete culprit, these geases tend to be something of a mystery to fulfill, their true solutions locked away somewhere in memory. An undead creature afflicted in such a way tends to have paranormal abilities and struggles to blend in with the living.

MAGICIAN. -1 Thirst, +1 Poise. Magicians, forever ignorant of death’s secrets yet always trying to pierce its veil. Most magicians don’t even realize the cruelty they inflict upon those creatures they summon, thinking of them as entirely their own creations. They take great pride in their craft, careful to make their constructs as lifelike as possible and viewing the corpse-lust of undeath as an unfortunate flaw that might be surpassed with enough research into the field of necromancy.

DEITY. -1 Memory, +1 Sight. Deities are sending living adventurers off on quests all the time. For their greatest secrets and mysteries, however, they only trust the dead. You may have been summoned to do something which, if it got out, could ruin your god’s reputation or cause a great schism among their followers. Or maybe the deity has already been long forgotten, with no living followers, turning to the dead as their last resort.

SKELETON ARMY. -1 Somatics, +1 Vigor Mortis. The dead are frequently drafted in wars between wizards, liches, and whatnot. At such a large scale, it’s only really possible to make broad gestures at what you’d like. Make a lot of them, make them strong, make them relentless. Point them at the other guy and hope they don’t get turned around. (Placeholder?)

AND MORE! These are just ideas for you to bounce off of, go make whatever kind of monster your heart desires.