As long as no consideration has exchanged hands or signatures signed, then yes. Contracts can be modified up to the second they are signed as long as both parties agree to it. Obviously, no one could negotiating away contract like this, but you always have the option to walk away.

During the closing in the finance office.

You can be asked all kinds of things. It's a little trick law enforcement tends to use: ask for things that the person being asked doesn't have any obligation to do.