Mom’s Boyfriend Died - No Will, Nothing - What Can She Do? Suffolk County, Ny.

Hi folks. Hoping anyone who knows the laws in. New York State or has dealt with anything like this could tell me what my mom can and should do here.

She’s looking for a lawyer but I’m just trying to help and get a picture of what she’s going to be dealing with myself.

Her boyfriend just died suddenly at age 70 after they were together 27 years. We tried and tried to get them to take care of some paperwork and they MEANT TO… and they never did. They bought the house together but only his name is on the mortgage or deed. He received Social Security and a retirement pension from a township maintenance job and has a large savings account they used to pay all bills. He has no will and never even filled out the forms on his bank’s website to make her the beneficiary. Nothing.

His only relative that we know of is a nephew he never really knew (his sister is already dead), my mother has no idea how to even find this guy to let him know his uncle is dead.

Is there anything she can do here at all? Or is she totally S.O.L.?
Any dos and don’ts for us?
Any idea how long she may be able to stay in her house?
Should she be looking for a lawyer or are they just going to tell her she’s screwed and charge her a thousand bucks for the privilege?

All advice is greatly appreciated.