I’ve just read the war below, a book on ww2 submariners, some of whom were considered KIA but were acutaully imprisoned off the records by the Japanese. Aside from emotional complications resulting from their reappearance, sone practical difficulties mustve arisen when they were rescued.
Tl;dr: By law, yes.
Public Law 77-490, officially, "An Act to provide for continuing payment of pay and allowances of personnel of the Army, Navy, Marine Corps, and Coast Guard, including the retired and Reserve components thereof; the Coast and Geodetic Survey and the Public Health Service, and civilian employees of the executive departments, independent establishments, and agencies, during periods of absence from post of duty, and for other purposes," but commonly called the Missing Persons Act of 1942, was signed into law on 7 March 1942 and dealt with the disposition of the pay and allotments of civilian federal government employees and servicepersons who were declared missing or missing in action, interned in neutral countries, or held as prisoners of war. Section 5 dealt with the making of a finding of death after one year's absence and the repayment of the six months' death gratuity to the government if it was being paid out or already had been paid out, and the civilian or serviceperson was found, in fact, not to be deceased:
SEC. 5. Upon the expiration of twelve months from the date the person is reported as missing, or missing in action, in the absence of an official report of death of the missing person, the head of the department concerned is authorized to make a finding of death of such person. Following a finding of death, the six months' death gratuity provided by law is authorized to be paid. In the event of the later return of such missing person to the controllable jurisdiction of the head of the department concerned, the pay account of such person shall be reopened and charged with the amount of the six months' death gratuity which may have been paid: Provided, That the head of the department concerned in his discretion shall determine a monthly basis for liquidation of the amount of the death gratuity so charged in a reopened pay account.
There's an answer relating to the US (although the answer doesn't actually mention it being about the US at all, just assumes you know) but what about in other countries? Like the UK? My mother's uncle was in the Royal Air Force stationed in Singapore and captured by the Japanese (although actually captured in Indonesia after he managed to flee Singapore). From what she tells me the family assumed he was dead until he was liberated after the war. I don't know if the family received any sort of funds though but if they did would they had had to repay? Or didn't the British do that?