Revenant

Revenants are an uncommon undead monster in various tabletop games, most notably Dungeons & Dragons, but also appearing in horror games like the World of Darkness and All Flesh Must Be Eaten. Based upon certain real-world mythologies, they are restless souls whose obsession with something or someone (stereotypically, murdering the bastard(s) who murdered them) is so strong they rise up from their grave, and in some versions they cannot be killed permanently; they just come back again and again until their driving obsession is nullified.

Revenants were promoted to being playable undead creatures in 4th edition Dungeons and Dragons meant to serve a purpose dictated by either the Raven Queen or some other divine/magical individual who gave them life in a body based on the corporeal form their soul once inhabited. They are not necessarily bound by the will of the person or deity who resurrected them, though; they have free will and are completely autonomous. A revenant's body's features are mostly similar to the previous life's, but the skin and hair color are ashy shades of gray or white or black and instead of finger/toenails they sometimes gain claws like talons. They don't always have a vulnerability to religion-based or radiant powers and are not inherently evil-aligned undead entities. They're weird and can be interesting characters depending on who's playing them and what the player's concept for the character is.

5th edition likewise made them playable in the April 2016 Unearthed Arcana article, which had a theme of "Gothic Heroes", adding the Revenant and the Monster Hunter and Inquisitive archetypes to the game. The 5e revenant is handled using the sub-race mechanics, where you take a base race and apply the Revenant's extra options to the base race. Of course, that doesn't solve the problem of how to apply it to Humans, Tieflings and Dragonborn, who don't use that system, but the document explains that quite handily, although it does leave it ambiguous if humans and dragonborn are supposed to get +3 stat points or not:

Human revenants increase two ability scores of the player's choice by +1 and get the Revenant traits. Variant humans replace their Skills and Feat traits with the Revenant traits.

Dragonborn revenants change their ability score modifiers to +1 Strength and +1 Charisma, inflict and resist Necrotic damage via their Draconic Ancestry trait (although they presumably keep the breath weapon type, so it's still a cone vs. line choice), and gain the Revenant traits.

Tiefling revenants get +2 Charisma and the Revenant traits.

Revenants in 5e gain +1 Constitution and the Relentless Nature trait. This represents their undying, goal-driven nature, so the player and the DM have to agree on a completeable goal that the PC is pursuing; this is what drew them back from the grave, and is important. Relentless Nature means that, when reduced below half of their maximum hit points, a revenant will regain 1 hit point each turn until they are at half maximum HP again. It also means that revenants cannot be permanently killed; if slain, a revenant will self-resurrect 24 hours later and no force can stop this. Even total destruction of the body won't do anything, the revenant will simply rematerialize somewhere within 1 mile of the place where it was destroyed. A revenant can sense the direction of their "goal target" and the distance to reach them so long as you are both on the same plane of existence. If you came back to murder the guy who killed you, then you know where he is. If you came back to protect your family, you know where they are.

Sound overpowered? Maybe But Relentless Nature carries a sting in its tail: if you complete your goal, then you automatically and irrevocably drop dead on the spot. With no further ties to the mortal world, you cannot be raised by any magic. So, your character will complete their goal, but that is it.

Coming back as a revenant is presented as a viable choice for players who have had a character die; you just adjust your stats as appropriate for switching out the subrace/core race traits, and then you crawl out of your grave, ready to resume your adventure.