You sit there and do nothing. The sherrif eviction backlog alone would take forever I would imagine.
The alternative is calling your landlord and speaking to him - almost as if he's a real human being. Tell him you'll have to move if he doesn't temporarily lower the rent.
First, in every municipality I've leased in, a landlord is only entitled to the rent from a broken lease up to the point where they find a new tenant.
Second, landlords can't typically collect rent after a date of eviction (same reasoning - you can't charge for a service you haven't rendered).
Third, rents are dropping across the US. It's not a given that they'll find another tenant immediately.
Fourth, the cost to recover rent is high, and usually not worth it.
do you have a citation for this? my experience in Boston in that landlords have stopped jacking up rents. that's about it. I haven't seen any come down yet.
In this case, housing assistance would mitigate any individually targeted evictees.