Damages in an unlawful detainer case is the term applied to rent which has accrued from the date the notice expires to the date of judgment. On an expired lease and 60 day notice, you seek possession and rely upon damages for unpaid rent (damages are the rent divided by 30 multiplied times the number of days since the notice expires)
If the tenant vacates prior to trial you no longer have an eviction, rather the case becomes a normal civil action for money
A proper response would require a thorough investigation into the history and background of this relationship. The information provided above is just that, information, to be used as you see fit.
You can amend the complaint now. Better now than later so tenant has adequate notice to defend amendment. Be sure you provide tenant or counsel with a copy of the amended complaint. Either side can appeal the holding, but landlords usually find an appeal more trouble than it is worth.
Actively practicing law in Texas. Inactive licenses in Arizona and Georgia. All answers are general in nature and no attorney/client relationship exists in this forum.