How does a drop in the local housing market lead to you losing your job? A general market crash causes many people to lose their jobs, it doesn’t discriminate against homeowners.
The renters are probably in a worse position in that case too, stop paying rent for a month and you’ll be evicted the next month. Stop paying your mortgage and the bank will at least work with you for a little longer.
Around here most management companies probably wouldn’t care.
These aren’t small mom and pop operations but companies with straightforward rules. You’d probably get an eviction notice before a human was in the loop.
Sometimes the cause is a loss of employment at a large local employer, and the effect is a drop in the local housing market as former employees try to sell and move to places with a better job outlook.