Yes the person can. This is considered what is called dissipation; dissipation occurs when one party uses marital funds for non marital purposes, and in this case, to fund an affair or any gifts that are given to the person he or she is having the affair with.
So, in this sense the spouse who is disproportionately giving away money or used marital funds for non marital purposes would then have to account for the other spouse, or would be entitled to reimburse the other spouse for this amount of money for what we would consider dissipated during that time. But this a very fact specific case and if you suspect that there is dissipation, then you should probably discuss this with your lawyer who again, has experience in dealing with litigation matters and is very comfortable with sending out discovery requests and dealing with litigation to try to find these assets.
Sean Sullivan is a family lawyer practicing in the Elmhurst, Illinois area at the law offices of Laura M Urbik Kern, specializing in child custody and dissolution in divorce. Visit his website, www.laurakern.com, and Divorce Magazine profile.