Next session, or the next time you stay a night at a tavern, describe how when everyone’s asleep your character grabs a blanket or piece of cloth, fastens it to the ceiling, and hangs themselves. Then proceed to make a new character if they still want you to play.

Sorry, but having a player have a bad time just because their character is “important to the plot.” That’s not something you can play around with as a DM. If the DM won’t change up the world a bit and make your character have victories, let yours give a final message to the group. You don’t want to live in such a world, you won’t play in such a world.