Now, after you've refused to rent to someone, and they wind up homeless, they land on the city's doorstep, and the city listens to their sob story, decides you are wrong, and suddenly you have tax audits, building inspectors, and enough alphabet soup to DROWN you in your life. 

I'd never want to cross any legal boundaries.I'm not certain as to what the exact legal definition of occupancy is in terms of tenancy, but from my point of view, an occupancy would be something that included a leasing contract, payment of utilities, delivery of mail, tenant implements their own furnishings, etc.

They give you a real street address and will accept packages and deliveries that require signatures.I also have a google voice number and gmail account. 

Mail it with delivery confirmation and go post it on the door with a witness or hand it to whoever answers the door.Immediately, give the subletting roommate a 30 day notice to terminate.  

The new tenant paid me monthly installments on that oil bill until it was paid off and ran low enough for them to start calling for deliveries on their own.

Maybe leave a bottle of it on their doorstep with a bow on it.

Same for paper delivery, UPS, FEDEX?

Send it with delivery confirmation.  

If your lease just ends without the necessity for a particular amount of notice, then you can just send her an email or letter with delivery confirmation that says that you just want to let them know the tenancy will end on X date and it is expected they will vacate on or before that date.If your lease says she has to give notice in writing to end it, and she hasn't, and you want to just end the madness, then just give her notice the tenancy will go to month to month as of August 1st - or whatever you want.You have the right to determine what happens when her lease ends.  

What you can do, is send notice via USPS mail with delivery confirmation.