I researched this very subject for my sister who has been divorced from her ex-husband for many years. She too has two children, none of whom could pay for their ex-husband/fathers funeral and he ex has made no arrangements. The local authority will fund a state funded funeral but they are legally bound to recoup the cost from the deceased person's estate if possible, so if he has any cash or property or retains a share of the family home the money will have to come from that. If any family member or friend wishes to have any part in the funeral arrangements they immediately become responsible for paying for it. If the state pays they arrange the date, time and place. Family and friends can probably attend but they have no say in it. It would be a basic cremation with just the hearse and no wake or gathering afterwards unless arranged separately by family/friends at their own expense.