Just remember, if you know what is required of you prior to departure, you will not take unnecessary classes abroad, nor will you have courses that may not be approved. With some planning, there are many possibilities. You can and will make normal progress toward graduation while studying abroad. You can stay in the host country for as long as you desire, if your visa allows it. Keep in mind that once the program has ended, you are solely responsible for yourself in every way.
Some students choose to stay an extra few months to travel.
By withdrawing from the EAP program, you are also withdrawing from the University of California at Davis. To better answer this question, you should see the CIEE brochure for more details. In some countries, though, a student visa is sufficient. This time period allows you to decide whether you will continue at this particular location or find housing elsewhere. School bulletin boards, the Director's office, and newspapers all provide information for people who seek housing.