So today, try to turn this question onto yourself, and turn it onto your fictional characters. What do you leave behind? How do you choose? What makes an object live for you or your character? Does he or she value concrete memory triggers like souvenirs (meaning "to remember" in French)? If your character had to leave everything but a few objects behind, what would he or she choose to take and why? It reveals a tremendous amount about a character to see what he would take in a fire or how much he wants to get rid of during a vigorous spring cleaning. Some people cling to their clutter with surprising desperation. They begin to link the memory with the object until they are convinced the memory will no longer exist if they lose the object. Keeping that souvenir, they think, is the only way to preserve events in time, to keep them alive.
And there are other people who have absolutely no sentimentality about objects, who find it all part of the trash heap of the world, all useless. This extremely practical approach can be taken to as neurotic an extreme as hoarding. Today, try thinking about what side of the spectrum you and your character veer towards.