There is no hard and fast rule when it comes to the number of days a person must stay. But with the mutual understanding, you could make the family member stay without paying the rent.

   First off since there is no original agreement to pay rent there is no enforcable contract that you can apply. Try evicting a squatter on that basis and you'll see what I mean.

 It depends on your lease agreement. If you signed a formal agreement, then there is probably an overnight guest section. In my lease, it states I can have no more than 2 guests overnight at one time, and anyone staying over 5 days needs landlords permission. They also cants stay more than 10 days twice in the year or else I will be charged $95.00 a month extra as they would be considered an additional tenant. Its pretty standard, though the amount may very.