Silly question but the fact that their mortgage expenses are fixed works to their benefit unless they bought at the peak, right?
Talking specifically about the big US city I live in - most landlords who already owned property since forever still jacked their prices up many hundreds of dollars in the past couple years because the market would bear it, not necessarily because they needed it to cover costs.
I'd imagine that the renters paying the largest rent (a few thousand, let's say) would be the likeliest defectors to buying a house. So buyers in the the top end of the market collapse, and those landlords begrudgingly start lowering prices - they can still make a profit. Maybe the low end stays the same.
I have zero understanding of the economics involved here, just pontificating.