The deadlines for the moratoriums have changed a few times. As of today, April 15, 2021, here are the most current dates:
Foreclosure moratorium ends on June 30, 2021.
Eviction moratorium ends on June 30, 2021.
Here is the White House Fact Sheet on “Biden Administration Announces Extension of COVID-19 Forebearance and Foreclosure Protections for Homeowners.”
These moratorium’s don’t cover every single property, but it’s pretty close.
If you want to keep your home, you’ll eventually have to catch up on those payments, either through a large cash payment, a loan modification, or a chapter 13 bankruptcy.
If you want to stay in the same rental unit, you’ll need to catch up on payments.
As for bankruptcy, yes, you can file bankruptcy to discharge the debt you owe on a rental, or even to surrender a home and discharge the mortgage debt. Of course, you should probably wait until the end of June unless you have other creditors trying to garnish or repossess. And yes, if you’re going bankruptcy on those unpaid rents or surrendering your house, you will have to move.