Your post does not indicate whether you filed a timely Answer to Complaint.
If you did file an Answer, the unlawful detainer case would convert to a regular civil case for damages once possession is no longer at issue (i.e. when you move out). The trial date would likely be set a few months down the road, and would not be proven at the UD trial set for next week.
However, if you did not file a timely Answer, the plaintiff at next week's trial can "prove-up" a judgment against you for restitution of the premises, the unpaid rent as set forth in the 3 day notice, plus holdover daily damages, possible attorney's fees, and court costs.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.