The true purpose is to allow you a safe window of opportunity for collecting your property from their house.
(This generally occurs within an hour or two of the breakup, but it can sometimes qualify as a sympathy-fuck even a few days later if circumstances are extremely bad)
Guy 2: I was bored and her dog just died.
Guy 1: Oh, so it was a sympathy fuck.
Girl 2: What? You gave him a Sympathy Fuck? He is going to stalk you now!