What game?
D&D would be hard to do this with.
Vampire, much easier.
In a game where power levels multiples better (e.g. 2nd level is nearly twice as good as first. 3rd level is more than 3 times better than first), you'd need to either:
1. Do a LOT of changing to the game.
2. Do a lot of changing to "first level" which would take away the whole point.
3. Expect that new characters are:
a. completely ineffective (which might be ok)
b. super min/maxed as much as possible for survival
c. all sneaky long ranged types to both survive and contribute
If you're talking D&D, i'd NEVER expect a defender / fighter who wasn't focused on ranged attackes to fulfil that role as 1st level among a group of 4th level and up characters.
Maybe cap the game at 4th level?
BTW. I don't mean to threadcrap, I just mean to point out that there are some really extreme challenges built into your question...BUT it could be done by changing EXPECTATIONS of players going into the game...sorta like in a Cthulhu game, you expect to lose/die.
One other ramification:
This will encourage selfish behaviors of survival among players who are higher than 1st level (and possibly suicidal behavior among new 1st level guys). Higher level guys will be LOATHE to die, while new 1st level characters will pale in comparison to the old character (and hence, players will not be invested in them).
One question: what is the reasoning behind your wanting to do this? I ask this because there may be other ways to reach your goal.
For instance, if you want a feeling of continuity, here is one way for players to introduce "new" characters:
1. Have hirelings in many adventures. These (or other NPCs) are statted out by players...heck, even the "bad guy" turned good could be used in this way. (This might also be a good way for you to alleviate some of your dm responsibilities). When a player dies, the hireling (usually of a level 3 or less than the pcs) becomes the new player character. Do this, and you have a "pool" of potential new pcs from which to draw, and it makes sense that they "step up" to join the party.