I can't imagine the banks wanting tens of thousands of empty houses. They might suspend our payments just to keep us in the houses to protect and maintain them. An unoccupied dwelling would become a liability to them, not an asset.
My son works for a commercial builder who had a $2.2 million loan on a piece of land that was supposed have an assisted living center built on it. The town council in that town refused to rezone the land, thus the builder has had to keep the land until another use can be found. The bank that was holding the loan got scared that the builder might walk away from the loan, so they approached the builder with a sweetheart deal. They took $600,000 and forgave the rest, just to get the loan off their books. I mention this because it is important to banks that their assets all be performing, with very little delinquency. In a SHTF situation, most banks would either fail, or they would accept much less than was owed to get out of bad loans. They will not want unoccupied houses with no potential to sell them.