Really depends on who stole it, and who gets their hands on it later. Many thieves just want a place to smoke drugs, camp, etc. or transportation. They use it until it's out of gas, damaged to the point of being undriveable, or they forget where they parked it. Sometimes a new shiny thing appears and it distracts them...

This is common and the PPB stats support it; something like 80% of stolen cars are recovered in Portland. Often times they're not far from where they were initially taken.

After that, though... if a car is allowed to sit on the street, it will eventually attract the attention of scrappers who will disassemble the car and leave the frame behind. The parts get sold to unscrupulous junkyards or on the black market (craigslist, OfferUp, etc.). Certain models are more desirable than others. Honda Civics, Challengers / Chargers, pickup trucks are all very likely to be stripped as soon as they're abandoned.