There are different sorts of Lasting Powers of Attorney but the base principle is that the individual is enable someone who they trust (the attorney) to make decisions on their behalf at a time when they are no longer able or lack the mental capacity to take those decisions. To that extent, if another person (the son/daughter in your example) owes the individual (with the LPA) a debt, the attorney is able to pursue it on their behalf.
But it surely depends on the nature / source / establishing the validity of the debt?
From where did the debt arise? - a loan?, an alleged gift? - the origins are endless.
And the planned use of the money is interesting - this does suggest a previous gift or transfer of assets to a sibling for the potential avoidance of IHT and which has now gone horribly wrong. Perhaps I am reading too much into it.