Can bank foreclose on property when property was refinanced by 3 of 4 owners, one of the owners never signed a Quit claim deed

Any lender who has a lawful lien on real estate may foreclose its lien, if the debt has not been paid or there has been another default such as failure to maintain, failure to pay taxes and insure, transfer of the property without the lender's consent, etc. Now whether or not that foreclosing lender will obtain and deliver full title at the foreclosure sale is an issue that lawyers and title companies may need to ultimately determine.

Assuming there was not evidence of fraudulent conduct, normally all record joint owners would need to execute a mortgage in order for a lender to hold a valid security interest in the property. However, if the owners hold title in the name of an entity such as an LLC, normally any owner with authority to bind the LLC would be able to execute a mortgage in the name of the LLC owner. Also, if the 4th owner was added after the mortgage attached by the three owners who held 100% title prior to the 4th acquiring an interest, then the 4th owner took title subject to the mortgage and the bank can foreclose. More facts would help in answering the question.