The situation is simple – your family won't get the Bitcoin if it happens that way. It's the same way that you (as owner) won't be able to gain access to your wallet or exchange if you can't remember your password to them. It's obvious a lot of people have died this way leaving their wallets inaccessible because they didn't get to reveal their passphrases to any family member. I'm one of those who believe that there's no way the maximum total supply of 21 million BTC will be feasible. A lot of Bitcoin will never be recovered because of such a scenario as OP has painted.