I assume your mother owned the home in a trust subject to a bank mortgage.
If the house is sold-any proceeds would go to the children if your facts are correct.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.
You should begin by securing a copy of the living trust. The living trust will identify the beneficiaries as well as the successor(s) trustees to your mother.
You should also check title on your mother's house. Is the house in the name of the trust? Even if not there can be a savings clause in the trust.
If the oldest child is living in the house and paying for it he could have a right of reimbursement (again one must look at the terms of the trust). He might also have the concurrent obligation to pay rent to the trust.
If the bank actually owns the house (has it been foreclosed on?) then the issues are moot.
This is a general answer only and you should seek the advice of counsel to address facts specific to your circumstances.
I think you have a fundamental misunderstanding of ownership and mortgages. The only time a bank owns a house is when they foreclose. When a person owns a home subject to a mortgage they own they home, but if they sell it they have to pay the mortgage off first. So if the house is sold the mortgage is paid and the rest of the proceeds go to the beneficiaries of the trust.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/