This is a pretty challenging idea to pull off, I think, depending on the number of players and your standards/goals.
You’ll have to pick a ruleset which provides enough traction to distinguish iterations from each other but is quick enough in practice that you can get through a lot of these “reboots” in a short time. (Anything where a fight scene takes 40+ mins to resolve is right out!)
If going a more traditional route (although this also would work well for many more story-oriented games or PbtA games):
One obvious RPG connection to make is to have the character’s “build” redone and/or advanced after each “death”. Allow the player to adjust the character’s stats, equipment, spell selection, moves, or whatever between each “reset”.
To take a rather extreme example, running a D&D character through a short adventure over and over, with the character starting at 1st level, and then leveling up each time they die, could be quite satisfying and exciting for some players, I’m sure. You get killed almost immediately on your first attempt, but as you come back at higher levels, the initial challenges become satisfyingly easy. (This is somewhat hypothetical, because in most editions of D&D, the gameplay would be too slow unless you were willing to do this over multiple sessions, but it illustrates the concept well.)
The other approach to base it more heavily on player cleverness, by having lots of challenges that reveal important information about them when you confront them. You hit these challenges and die, and, in the process, learn how to overcome them in the future. A series of deathtraps is one such example: probably and almost certainly lethal the first time you try, but easy to overcome once you know what they are.
To make it satisfying from story/character development perspective, on the other hand, you’d want to include opportunities for character growth/change, on one hand, and story development/discovery, on the other. Each leg of the “story” should develop one or the other further, which you don’t get from just running through the same adventure over and over - you need dramatic developments on pretty much each run-through, which means new information and new catalyst for character change.
I’d advise you to choose one of those options and hit it hard; trying to do all of them at once might be too much of a tangled web to be realistic unless you have a LOT of time to figure out how to do it.