A prior renter in our home who paid some (not all) rent is threatening to sue for equity. Is this possible?

An ex girlfriend of my fiancee's lived in his home (which he has the title for) for approx. 1 year. She has since been evicted and is threatening to sue us for the equity in the home. When she was evicted, she took all of what she bought, except for the carpet. A judgment has been offered in her favor for the carpet, that's not what we're concerned about. Should we get an attorney for this? Is this even possible that a renter would be entitled to equity on a property? There was no rental agreement, and there is really no proof that she was even paying rent during that time. Please help!