If (person A) wrote their will in1970 leaving a property to (person B) who has now recently died, who does the property now belong to?

That depends on whether person A is still alive. If they are, the property still belongs to them.

If person A died before person B, then the property passed to person B. If person B has now died, the property passes to whoever is named in their will or, if they did not leave a will, it will be subject to the laws of intestacy in the country/state where person B was domiciled.

If person B has offspring or a spouse, it will almost certainly pass to them.

If person A is still alive, the bequest in his will died when person B died UNLESS the will specifically says what happens if person B predeceases person A. My will deal with such things. So should any will.

If person A now has Alzheimers, it is not obvious why the courts would grant power of attorney to those who *would* have been beneficiaries under person B's will. For the reasons stated above, they might not be entitled to anything under the will of person A. They either have no interest in the well being of person A or else they have a conflict of interests if they think they will in some way benefit under his will. I think the surviving beneficiaries under person B's estate would be hard pressed to justify the grant of power of attorney.

You've worded this in a way that's open to several interpretations.

Alice owns a property free and clear. In 1970 Alice wrote a will leaving the property to Bonnie.

If Alice dies before Bonnie, and Alice owes no money to anyone, Bonnie gets the property, assuming the will is legal.

If Bonnie dies before Alice, Alice needs to rewrite her will. If she doesn't and she dies with the original 1970 will, it becomes a nasty battle between Bonnie's heirs and Alice's heirs and will come down to state law, case law, and the specifics of the will.

The will does not become effective until "Person A" dies. "Person B" and Person B's heirs have no entitlement until then. Person B's "beneficiaries" (whoever that is) cannot get POA for Person A just based on "beneficiary" status.

If Person B predeceases Person A, then assets would go to any other heirs named in the will. Person B's estate gets nothing. If there are none and the will is silent, then state probate law determines how the estate is settled.

IF person A still owns the property, and it doesn't need to be sold to settle debts, than person B inherits it as per the will. If Person B is dead, then the legal heirs of Person B would end up with it.

Also if Person A has Alzheimers , can person B's beneficiaries get power of attorney to be able to pay the bills and deal with the estate.

I'm guessing person A's other heirs or next of kin followed by person B's.

B's heirs.

Your next of kin