Yeah, it would be a case of the player dying. I thought the Ghost Shooter multiplayer demo just re-spawned you at a different position on death, so I wasn't sure how the Multiplayer object handled object destruction. I'm designing the game to be match based, so the players start in a chat lobby until the host starts the game. Once the player dies in the match, they still get to watch the match to its end, at which point I'll probably throw everyone back to the lobby to start a new match if they want.
After playing with it, looks like hiding the player object is the only option unless there's a way to disassociate the object after it's been associated. I'll have to go through and add a check in a few events to disable all interactions with the "dead" player and cancel out inputs, collisions and bullet overlap checks (does disabling a Sprite's collisions disable overlap checks as well? Overlapping at Offset seemed like the easiest way to test for bullet collisions with lag compensation). Bit more work, but not too bad.