BP friends, I am in possession of a coop in NYC suburbs.  

You can always start paying taxes and take care of property and try quiet title or adverse possession, but that’s a risky game to play.

Offer accepted on my first deal (triplex) and inspection pending (WA State).During my initial walk-through, I met a couple who seemed to be more than knowledgeable about the property, possessed keys to storage areas (possibly other units too), had special parking spaces, and stated that they take care of the things around the place including the large yard in exchange for lower rent.

Question is , if i cant get a hold of him, how do i start cleaning up water damage, and can i assume he is not coming back to claim his possessions?

    An investor in my area had about a dozen properties that were for sale off market, I made my first round of offers on each one and before the seller could counter the agent informed me that the bank was taking back possession of all of them. 

I know this isn't a increasing question persay but certainly might require that brilliant outside the box thinking I know you all possess.

Can also hint that I might consider adverse possession with the white fence likely being 20+ years old as grounds for him working with me the preferred way.

Roman is correct, except the tax certificate/deed route doesn’t give you possession....it just sends it to public auction where you have to bid against everyone else.

RIGHT OF TERMINATION AND RE-ENTRY:In the event of any breach of payment of rent or any other allowed charge, or other breach to this lease, Landlord shall have full right to terminate this Lease in accordance with state law and re-enter and re-claim possession of the leased premises, in addition to such other remedies available to Landlord arising from said breach.I already reached out to her and told her she needs to get the pets out of the property of which she replied that it was for a friend who was out of town for the weekend and the pet will be gone today.What can i do if i find out there are still pets in the property.   

These tenants have possession of the house, therefore any damage to it is their responsibility.