In California (Los Angeles, specifically) does a person have to move if they are named in an Unlawful Detainer action, they answer the Summons and Complaint and appear, and the judge rules in their (the Defendant’s) favor? If so, can anyone please point me to any statute(s) and/or case law that would illustrate such an outcome? Thank you!
The short answer is no. You don't have to leave until the term of the lease ends or you are required to move based upon some new default under the lease.
I'm not sure that there would be case law exactly. The default rule is that you don't have to move unless there is a reason that you have to move. The landlord brings suit under the law to get an order from the court granting the landlord possession and evicting you. If that order isn't granted, the landlord is back where he started without a right to evict you, which is the status quo.
If you were forcibly removed from the premises by the landlord without an order (particularly when it has been legally adjudicated that he doesn't have a right to evict you), you would probably have grounds to sue the landlord for wrongful eviction and there might be criminal charges that apply as well against the landlord and everyone who participated in the wrongful removal.