If the tenant loses the case, but needs more time to move out, he or she can first try to talk to the landlord to see if he or she agrees to let the tenant stay a little longer.
If the landlord does not let the tenant stay longer, the tenant may file a Request for a Stay of Eviction ("Stay") and set an ex parte hearing. If the judge lets the tenant stay longer, the tenant may have to pay the rent for that period of time. The amount of time the tenant can stay will depend on the case.
For more information and resources may be able to assist you, please refer to the Notice That You Have Been Sued that was mailed to you at the time of case initiation.