The power of attorney does not replace a Will or vest an interest in property. Instead, the Power of Attorney is an authorization for one person to act on behalf of the other. While theoretically the grantee could use the power of attorney (during the grantor's lifetime) to transfer property from the grantor to the grantee, they would potentially face problems with someone complaining that the power was abused by self-dealing.
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It sounds like you are asking if a power of attorney remains effective after the principal is deceased. Generally, a power of attorney expires upon the death of the principal. After the principal passes away, the duly appointed representative of his estate handles his remaining affairs.
The foregoing is a general answer based upon limited information, should not be construed as legal advice advice, and does not create an attorney-client relationship. It is the opinion of the writer alone. The author is licensed in Indiana and Ohio attorney only.
As the other two lawyers stated, the power of attorney dies when the principal (the one giving the power of attorney to someone else) dies. And a power of attorney is not a will. So if the principal dies without a will, then their estate will be probated through the rules of what is called "Intestate Succession." If this is in Arkansas, that generally means that the "issue" (children or grandchildren) will share the estate, with the spouse being able to take an interest. I don't want to get into more detail than that, because you really need to talk to a probate lawyer -- someone who handles wills and estates. They can advise you on what needs to be done to open an estate for the parent who died, to appoint an administrator, and to distribute the decedent's property.
No attorney-client relationship is established with this answer. It is not to be considered legal advice, but is merely given to point you in the right direction and give you a general answer as to the law regarding the question you have asked.