I got a chance to read this judgement recently.

Finding where they moved to to serve them notice can be tough.After you serve them, you can take all your evidence to court and ask the judge for a money judgement.  

Also, what if you don't evict but you have a tenant that leaves owing money how does it work, do you have to sue in small claims and get a judgement first?

It would be a toss up if you would get a judgement, given the facts you've shared. 

Quote from @James McGovern: If you got a judgement against a former tenant in a Connecticut court and the tenant moved to North Carolina.

After the latest judgement in court the tenant knew they lost, but didn't know the timing of the physical lock out. 

Quote from @Terrence M Brannon: Quote from @Peter Walther: The low judgement amount vs the estimate market value leads me to believe these may be HOA or COA foreclosures in which case 1st mtgs will survive and the purchaser will be taking subject to. 

I’m still new to this so I don’t have the experience to make an educated judgement here.What do you guys think?

At the same time take her to court for eviction, all rent and get a judgement.

It could be when the foreclosure judgement is entered, When that same judgement is docketed, when the deed is signed, when the deed given to recorded and receipts for all payments received, or when the deed actually shows up on record.