If a veteran dies after filing his or her application for a home as provided in this chapter, and his or her application is subsequently approved, his or her unremarried spouse may, in the discretion of the board, succeed to his or her rights, privileges and benefits under this law that would have been his or hers but for his or her death. The contract or purchase which the board otherwise would or might have entered into with such veteran may be entered into with his or her unremarried spouse.