I currently live in a fourplex, living in one and renting out the other three, and the tenants tend to keep to themselves (thankfully).Just buy right and make sure you have decent tenants with full-time jobs who are too busy to bug you for every little thing.I could see how it could be more of a nuisance with larger properties but with 2-4 units?  

It should be a monetary slap in the wrist....a nuisance, not an opportunity for profit.Also, circumstances can play a part.  

This can be considered an "attractive nuisance," and you can be held liable, especially because the property is not fenced.People can still sue you, regardless of your hold-harmless clause. 

If this continues the other neighbors could call the police for public nuisance/disturbance and after so many times, you may be fined as the property owner of the unit. 

They can be what's called an "attractive nuisance," which is something that draws kids onto the property, and if they get hurt, you're negligent, if you hadn't taken steps to keep kids from getting to it.  

Anything else I am ok with so long as it does not become a nuisance.

Now, on the other hand if these obstacles don't apply you could apply a myriad strategic ways to either have her removed or clean up her act, literally.I'm thinking public nuisance, you've already stated that after your taking ownership, renters left, we imagine it was because of her.

Most of my properties are at least 100 yards from my home, so I'm not going to camp outside a tenants house to try and catch them out.But I'd consider it not because of the nuisance of ferals, but that cats especially have dreadful lives as feral cats.

Its likely that they are being abused as a lot of the nuisance noise is them running around and/or crying/yelling.

Those are nuisance (grass cutting liens), demolition, sewer assessments, lighting assessments, library dues and fire association dues.