can medicaid take a home and the mortgage too?

What is the name of your state (only U.S. law)? Massachusetts

My mother, a current recipient of Medicaid is facing the possibility of entering a nursing home for extended long-term care.

I understand that upon her death Medicaid has the prerogative to force the sale of the then unoccupied home and recoup some of their expenses.

The home has a $50,000 lien on it from reverse mortgage payments that my wife and I have been providing to my mother through a 3rd party reverse mortgage company over the past 5 years.

Can Medicaid take the home....and usurp the current first lien we have on it ? Has this ever happened? If so, how can Reverse Mortgage Companies or banks afford to give loans to the elderly?

Not a lawyer, but I think you may find that the state will use the monthly reverse mortgage money as money that she will need to pay each month for the nursing home. She'll also pay a goodly chunk of any social security or pensions. Then when the home is sold for the estate, and the lien is paid off, then any remaining value will be claimed by the state as well (up to the limit that the state has paid for the nursing home care).

This is of course, after they've done the analysis on the 5 year lookback, and make sure that the asset base is spent down on the nursing home till she gets below the state allowable threshold.

As soon as she moves out of the house, the reverse mortgage becomes due and that will most likely result in the sale of the house. There isn't any "monthly reverse mortgage money" at this point, just whatever equity was left in the house.