No, Fed Ex would not have to pay for the loss of your apartment for two reasons. First, the terms you agree to when you ship with Fed Ex limits their liability to a return of the shipping cost. In shipping with them, you contractually agree that is all they are responsible for. Second, someone is only liable for the reasonably foreseeable consequences of their action or failure. It is not commonly the case, and therefore not reasonably foreseeable, that a lost or delayed package would cost someone their apartment, and so they would not be liable for that.