I told him face-to-face in no uncertain terms to stay off my property and I was prepared to involve authorities if necessary.As @Marcia Maynard says you will need to be very diligent about monitoring the state of the property.

It has two...an oil monitor (with new filters) and the wood stove (common in the area) She refuses to use the wood stove and says she cant afford to buy oil.I served a 30 day notice which was she claims is invalid as it wasnt signed by me...but for me. 

Regular inspections to change HVAC filters, etc can take place to monitor the residence but just the advance rent alone wouldn't scare me off.

If you do have mold where she is staying make sure you have completely remove the mold and monitor it.

Companies like SimpliSafe have deals going on frequently for various packages, subscriptions are economical for 24 hour monitoring.

Otherwise you have nothing to cover damages.I make my pet deposit/fee (I didn’t know the distinction) $250 per pet, of which $100 is refundable to give them incentive to monitor their pet.

(They monitored it).

I learned right away to monitor my credit.

It's been my practice to keep these tenants for 3 months and monitor them closely.

It just seems too expensive/cumbersome to really monitor/analyze exactly what you're lending on, etc.