Character death is the most common reason a player will write up a new character for use in your campaign. But it is not the only reason. Sometimes a player will choose to retire their character in order to role-play something more relevant to the setting; or to choose a Class more in line with their style of play; because of conflict with the Party; or because the character offers the player no opportunity for advancement or growth.
Often times, when a player in our group retired his character, the party and the DM assumed that the character just walked away from the adventuring lifestyle and was never heard from again. There was a clean break between a player’s outgoing and incoming characters.
In D.W.’s 2nd Ed D&D game, player C.U. decided to retire his high-level, wealthy, morally-suspect wizard and start a new character. C.U. then asked the DM if it would be okay if his new character could happen upon his old character out in the wilderness, and murder the old character and take his magic gear and other possessions. Then the new character would meet up with the party and join it. D.W. said no.
In the days of Heroes Unlimited and the Palladium RPG system, player P.H. would often (very frequently) have his “favorite” character killed off by enemies or (very frequently) other players’ characters. For a few minutes he would bemoan his terrible luck. Then he would erase the late character’s name on his character sheet, write in a new name and change nothing else, and claim that this “new” character was the old character’s twin brother.
How and when a player introduces a new character to the campaign is at the DM’s discretion. Most often the new character will join up with the existing party as described in CaSE #22, unless the party’s location or place in the storyline otherwise prevents a new character from appearing and teaming up. Same too with the timing; a DM may choose to delay a player’s re-entry to the game until the party reaches a town or a specific point in their current plot or sub-plot’s arc.
Consideration must be made regarding the old character’s possessions, and claim to Party Treasure. If the old character has died, are their possessions added to Party Treasure, interred with the body, lost with the body during the death ? Can the new character lay claim to some or all of the old character’s equipment ?
Lastly, a DM should enforce the divide between Player Knowledge and Character Knowledge; a new character will only know details and information that he or she obtains from other characters or through his or her own research. A player should not be prevented from starting a new character to replace a character that is no longer enjoyable; but the new character should come with some disadvantages given their context as an outsider to events in the party’s mutual history.