I am sorry to hear about your father's death.
Are you certain that your father's estate is insolvent? The fact that he was in arrears with his mortgage payments does not necessarily mean that his estage is insolvent.
If your father's estate really is insolvent — i.e. if all of his assets, including the house, would not cover his debts — then the situation is very messy. Your best course may be just to abandon the estate; there's nothing in it for you. You'll have to pay for his funeral yourself, but you've probably already done that. But don't do this unless you are absolutely sure about the insolvency; it may pay you to look very closely at your father's affairs, and to consider whether there might be any possibility of challenging any of the claims against his estate, or of negotiating a settlement of them for a lower amount than is due.
If you do decide you have to walk away, then any of your father's creditors can apply for a grant of administration so that they can collect his assets, sell them, and pay his debts at least in part. The lender who has a mortgage over the house will probably do this, since it's the only way they can recover any money.
You should tell the tenants what the situation is. They should not pay the rent to you (and if they offer to you should not accept). If a creditor does take out a grant of probate they can (and will) start collecting the rent and will look for arrears; it would be wise for the tenants to set the rent payments aside so they can meet this demand when it comes. The creditor who takes out a grant will also serve notice to terminate the tenancy so they can sell the house.
If no creditor applies to take out a grant of probate, the tenants can stay in the house indefinitely (since nobody has a right to evict them) without paying rent over to anybody (since nobody has a right to demand it). If this state of affairs continues for 12 years the tenants can then set in train the steps needed to assert title to the house on the basis of adverse possession.