When a character who becomes a Spirit is unsuccessful at returning from death, they are permanently deceased and the character can no longer be played at that event. From the Accelerant core rules:
"If the spirit cannot return from the Death Area then the character passes beyond this world and is said to have taken a final death. Final death means that you can no longer play the character in question, and adds an air of danger to the game by threatening your in game persona."
What happens to a player after succumbing to a Final Death can vary by game setting. A player may be asked to join the NPCs and take an NPC role for the remainder of the event so that they can still participate in the game until they've created a new character for the next event.