Is there a law in MA that enables Elder Services to be able to step in and place a parent with dementia in a nursing home?

Part of your concern seems to be that you were not asked to be present, yet you say your mom is completely cognizant?

APS has no way of knowing of your healthcare proxy, do they?     Unless mom said " I'd like my daughter to be here. Please call her and let's set up a meeting" or, " let me get my daughter on speaker phone".

When an elder with dementia wanders, the person is a danger to himself.  The state has the right and duty to step in and protect your father.

In most states, if there is a spouse in the home, it can't
 be sold while the spouse lives in it, so your mother would have lifetimes rights to live there. But a lien would  be placed by Medicaid to recoup payment for services.

Is this what your mother reported to you?

Call APS for clarification.   Did mom get a business card from the person who visited?

I would cooperate with them and ask for the help in getting more assistance for your parents.

What is your immediate plan for keeping dad from wandering, I.e. safe?

In Mass, I do not know. Medicaid is administered differently in each state. But, yes adult protective services has the responsibility to ensure that the elderly and other incapacitated people are receiving proper care and are safe. They do not have the right to sell the home to pay for care. Under Medicaid a home and one car are exempt assets. However, Medicaid will place liens on the house for future reimbursement of care provided under the program.

It is s best to cooperate with APS they are trying to help. Maybe mom is not able to provide the necessary care any longer. Do you live with them?