not a lawyer but my understanding is that they will attempt to collect the debt from your estate (cash in your account, assets you own). they get dibs before your family and will take everything they can to cover the debt. but if your net worth is less than the value of your debts they won't go after your family. but your family will also not receive anything from your estate even if it is in a will.
again I'm not a lawyer though so it would be best to seek advice from a solicitor.