My mother in law is in a Nursing home in PA. She gets a pension and SS. Should her SS and pension be going to the nursing home?

If she is on Medicaid, it is highly unlikely that both the Medicaid department and the NH don't know about her pension and social security checks.

When in a NH and applying for Medicaid, some people choose to have the NH as the payee for their SS and pension. Some choose to keep the checks being deposited to parent’s bank accounts, receive a bill from the NH, and pay it the bill from the bank account. I chose the latter so I was sure that the money was coming in correctly. It gave me more control of it. My friend chose the former method and found out months later that SS had decided her parent had passed away (not) and had stopped paying the NH. She spent months getting it straightened out.

Yes, her Social Security and pension need to go to the nursing home because both of them probably won't be enough to cover the cost of her care. Medicaid will pay the rest.

All of her assets need to pay first, then Medicaid pays, as I understand it.

If she is on Medicaid, pension and Social Security should be going to the nursing home.

So, if she has Medicaid, she has an assigned "share of cost" which is the total of her income each month, minus her "personal needs allowance".

Who is in charge of her finnances? Is there a spouse?

yes she has Medicaid,

What does the admission paperwork say?
Who signed for her admission as the " responsible party"?
Is she on Medicaid?
Does she have long term care insurance?