Adverse Possession

You can't buy it or take over title if it's not for sale and it has not been foreclosed upon (so you could you negotiate to buy it from the government or bank--whomever foreclosed). The fact that property is not in use or "abandoned" has no effect on its ownership, so long as the taxes are paid so the govenment does not foreclose and the mortgage is either paid or the lender is not, for some other reason, foreclosing.
If you want to pursue this, try to find who *will* get it, if anyone. It is likely there is someone who will inherit under a will or, if no will, under the laws of intestate succession. Research in the surrogate's or probate office for your county to find its status: is it in probate? Is there a will? Is there personal representative of the estate (either executor or administrator)? Once you know that status, you may be able to determine who to approach about buying it.
Also contact the lender: do they know who will inherit? If so, they may be able to provide that to you. If to their knowledge there is no one inheriting (no will, and no relatives close enought to inherit under instate succession (the rules for who gets what, when there is no will)), then ask if they'd be willing to sell to you if they foreclose: if no one is paying the mortgage, they may be paying the taxes to keep the government from foreclosing while they figure  out what to do, and if they know they have a buyer, may be willing to foreclose, then sell it to you.
But again: you need to think in terms of finding out who has the right to the property and making an offer for it. You cannot "take over" title to property, even if abandoned--even if the government had foreclosed, for example, for nonpayment of tax, you'd have to buy it at auction or otherwise from the government.