A child who has lost their father should check for any PPI policies as they may not know if any existed. If there is evidence the father had a PPI policy the child can put in a claim for PPI. To do this they must prove they have the relevant authority as an executor (if there is a will) or named as next of kin.
If the father left no will, the rules of intestacy must be followed, and the child will have to apply for grant of letters of administration. Once they have this, they will become the administrator of the estate.
The child will need to apply to the insurance company for them to pay off outstanding debts under the terms of the policy. Any payments from a successful claim are not made to the child directly, but instead are used to pay any outstanding debts on loans and credits cards for example.
Any debts that may have been settled before discovering the PPI policy, which could have been paid off through a PPI policy can be reimbursed later after completing the right paperwork.
If a claim under the PPI policy is rejected, the child should do a check to see if the policy was mis-sold. As the child is an agent of the estate, they can claim for compensation on behalf of their father and use the money to repay the debts.