Well, it sounds like fraud. I’m not sure of the distinction you are trying to make between the mortgage and the bank? If the borrower falsified his/her own documents, then it is known as “fraud for housing” – meaning, the buyer lied in order to obtain a home and a mortgage for which he/she should not have been qualified. If the mortgage originator or other professionals (who might have been a mortgage lender, a bank employee, a mortgage broker, an appraiser, an attorney, a real estate agent) falsified the documents FOR the buyer, without the borrower knowing about it (rarer, but it does happen), so that he/she could make a profit by writing the mortgage or selling the house, it is known as “fraud for profit” – also known as insider fraud, as it is perpetrated by a lending professional for personal or company gain.
I suppose you could further classify it by what sort of mortgage outfit originated, underwrote, and funded the loan … but that isnt clear from the question. Any way you look at it, though – the person that lied committed fraud. A lender that should have reasonably suspected that the information was a lie, or didnt actively verify the borrower’s ability to repay the loan, as they should have, could also be accused.