What can adult children do to keep their late mother’s house if they are still living in and paying on it?

First of all, the best thing to do is get the house transferred in to your names (although you do not have to for mortgage purposes if she had a Will, see below). This can be done so long as your mother left it to you all in her Will. If she did not have a Will, then she died "intestate" which means that the intestacy laws of the state in which she was domiciled as of the date of her death will prevail. Typically, this means that the heirs would be the survivng spouse, if any, and their children. If there was no spouse, then the children inherit all of their assets in equal shares. A probate filing should be made to do this. Once done, you can then keep on making the mortgage payments as you have been. By way of explanation as to the status of the mortgage, a mortgaged property can be inherited just like any non-mortgaged property. However, when a property changes ownership, typically the mortgage lender has the right to demand full payment of the entire balance of the loan. That's because most mortgages have what are known as "due on sale" clauses which allow lenders to call a mortgage balance due if the home changes hands. That having been said, an inherited property is exempt from this type of clause. Lenders can't call a mortgage due if the home transfers either to a joint tenant, a tenant by the entirety, or a family member or members. The mortgage stays in place and the person inherits who has to make the payments. Note: The lender might require the person(s) who inherit(s) to officially assume the loan, which means personally taking responsibility for it, although it can't deny them the right to keep making the mortgage payments. Accordingly, it can't force an inheritor to refinance the mortgage into thier own name. In fact, they can keep the property in the deceased's name if for some reason they wanted to so long as they inherited under a Will (intestacy is different and a probate must be filed). Since the law varies state-to-state, this is just a general overview. At this point, you should consult directly with a local probate/real estate attorney; they can best advise you further.