The insurance terms can be found here -> https://www.aigtheftandloss.com/coveragedocs
The coverage technically applies to the person who purchased the coverage with their device. So your family member is the only one who can file the claim. They would likely then have to explain why it was lost or stolen where it was which would open the question of was it or wasn’t it in their physical possession at the time of loss or theft.
I read those terms as also indicating it would have to have your family members AppleID signed into iCloud with Find My enabled or the coverage would be void. Their AppleID is not yours, so that would be another sticking point when filing a claim.