The banks usually hire a Realtor to sell the property who will hire a contractor to get rid of the stuff. Some may go home with the Realtor, some with the contractor, some to goodwill perhaps, some to the dump. It has to be clearly abandoned which usually means over 30 days. If there is any doubt they will send out notices to the last know address and posting a notice of abandonment to the house. The contractor/ bank will store it off site or may just let it sit there 30 days.
I go to garage sales every week and have met a few contractors who actually take the stuff to their house and sell it. I have gotten some good bargains like full bottles of propane for a buck and gallons of antifreeze free. One guy does all the Hud homes and he has tons of stuff almost monthly.
Good luck and thank you,
Ted P. Stokely Jr
11505 Sw Oaks
Austin, Texas 78737
512-301-9171 home
512-587-6177 mobile