If they’re not being played by the player, they’re an NPC in that campaign to be used by the DM as the situation necessitates. I don’t see that as particularly controversial. If the PCs are never in a position to encounter that character again, fine. If they do, however, the character is now the DM’s responsibility since the player who used to play them is either gone or has moved on to another character that now serves as their PC. Giving up playing a PC, as I see it, automatically relegates them to NPC status for as long as that situation persists.