The Suitcase

From the introduction:

The Suitcase is a letter-writing RPG for two players. You will need something to write on, a few common objects, and a box (or, even better, a suitcase) to store them.

The players will alternate in writing the thoughts of a shared character, who has amnesia and who tries to gather their memories, using objects they found in an old suitcase. One player will try to make the other one discover a secret of that character. The second player will try to make the first one discover a major failure in the life of the character.