I was poring over the D&D official Monster Manual, and I noticed the section of the undead. There is a creature called a Revenant. Revenants (for those who may not know) are creatures who were slain wrongly. The spirit of the dead returns to its former body or the body of any humanoid. The point of the Revenant's existence is to exact punishment on the person who killed them wrongly. No matter the form that the Revenant takes, it's rival can recognize it without a DC. The Revenant dies after it has killed its rival, if it is killed, or after a year, when the magic that binds the Revenant to life expires.

My question is this: Can players turn into Revenants and other undead? If so, what are the rules for this. I can't find any rules in guidebooks, but there is also no rule stating that players can't turn undead. I know players can turn into lichs, but turning into a lich is voluntary, and most other types of converting to undead aren't. Please answer to this as soon as you have an answer, because I have a session tomorrow morning, and I would like to be prepared beforehand.

The answer is yes. But I'll have to relocate what book it is in and edit it here in a second, unless someone else beats me to it. 

What you are looking for is the Reborn Lineage from Van Richten's Guide to Ravenloft.

https://www.dndbeyond.com/races/706719-lineages

Outside of a Dimension of Dread, the answer would still be yes, though they would no longer be player characters.

That is, yes, it is possible. Depending on the DM, they could become a Reborn (as shown above)or they could simply become monsters, and therefore under control of the DM.

There are no fixed rules on it, however (even the basics of how they become reborn), though in some cases the monster that kills them may have some aspect of how that happens (been a while since I looked, but there used to be a plant that created zombies through spores).

Alternatively, they could be raised through necromancy. A lot of it depends on the world you are using and how the undead work there. THe rules are absent so that you can come up with a way to make that happen yourself, if you want, or to simply say it isn't possible.

IE, your call, no matter what.

 Thanks!

Spoiler! The first campaign of Critical Role had one of the characters turn into a Revenant. 

I believe the Tal'dorei guide has a Hollow One race that can be used as well as the Reborn lineage from Van Richten's. 

You could also just make it part of your campaign if it happened. Just rule they return as a Revenant. Then they can play that same character until they are able to finish their objective. Just make a few changes to fit your game ( I personally would rule the heck out of it so there is an understandable structure to the now Revenant race). But I could see that being very cool to a game.  Leads to an epic battle with the Revenant's main foe. And he dies in the end killing the villain.

if a player was slain wrongly then i don't see why they wouldn't be eligible. If a player fits the criteria then it should work.

Would interesting game play. One would think their specific goal would be to exact revenge. No side quests, no need to rest, east or interact. Of course, the DM could determine that their hunger burns at every delay and could even have some sort of table with negative side effects. There could be some interesting endings as well. Does the revenge exacted cause them to finally rest? Do they continue in their undead form without purpose? Do they in fact have freedom to think? Again, in D&D the DM can make that determination.

I can't seem to find a way to use the Hollow One race, either on a new character or converting a current character from another race. It simply does not show up as an option? Does anyone know how to get this working?

Do you own Tal'dorei?

You will only be able to access that race if you own the Critical Role sourcebook it's from or you're in a campaign with a master tier subscriber who owns that book and has turned on content sharing.