I like to bring in replacement/new players with the idea that their character is integrated into the world more so than what I required in the initial application.

For example, characters are working with the city guards, well a new character would be assigned to keep an eye on the PCs or PC are investigating a crime, the new PC may be a witness; one who was involved with the victim; or even the one that is trying to cover up that crime.

I think it's important to give the players the feeling that the world is alive and a PC simply coming from out of the woodwork to join up can be too much suspension of disbelief. I want to make the integration as organic as possible.

I'd also give them the choice to take over a non-important PC that the players have encountered.