The high rate of gamblers who take loan for gambling purposes is quite alarming, and most of them are fathers to kids. Most of them don't end up taking care of their debt before passing. What happens to the funds, when the lender comes for his money? It's quite a tough one for a person who isn't a gambler to inherit a trouble from a gambling dad. Such things also increase the anger of the society on gamblers, because the addicts are, also, good at extending their problem gambling to other close relatives. Could it be talked through in the law court?
Let me start by saying it's highly irresponsible of any father to be collecting loans for gambling, it is just unspeakable and will truly anger the children especially when they are not following his gambling path. Fathers should be saving and preserving assets for their children, and not otherwise. But still, it is not as thought and obliging as you think, it is subjected to many considerations.
When you take a loan and couldn't pay it until death, no one is responsible for the payment other than you unless there are signed legal documents to back the transfer of payment up which could make another person than the direct debtor liable for payments. For this, the children are never responsible for the collection of the loan, so they can't pay the loan unless they are legally involved. But at times, to avoid shame or just want to clear the name of the father to honour him, they might choose to pay off the debt.
Also, in the case that the debtor uses certain assets as collateral, the creditor will come for the asset to either take possession of it or sell it and set off the bet if anyone can't pay the debt for the deceased. In this case, as well, the children might not want the asset to be sold and be forced to pay the debt. I hope you get the gits? Inasmuch as the children are not co-signers to the loan collection, they are not responsible for it and will not be obliged to pay unless they feel like due to one reason or another. This is one of the risks that banks and loan companies face too if they do not properly document their clients/customers to make them accountable.