how long can the heirs stay in a home that has a reverse mortgage, after the borrower passes away

Reverse Mortgages are due and payable at the time of the owner's death. You obviously will be given a reasonable period of time to get a new mortgage or sell the property. If you are the heir and don't qualify for a mortgage you will need to sell the property. If this is your situation, I would suggest you speak to a Real Estate Attorney to see if there is anything you can do to protect your ability to keep the home. I would also speak to an Attorney if the mortgage is more than the property is worth and you would like to buy it - you may be able to negotiate buying it at market value, not the mortgage balance.