Hi -- Sorry to hear of your Mum.
The debt that she had in her sole name has to be written off if there are insufficient funds from her estate, however they could technically claim that her share of the house she left is an asset, but rarely does it come to that if there are no other means of repayment. I must add that if the house was owned as "joint tenants" by your parents that rules out the possibility of the creditor making a claim on the house, in that case the property never becomes a part of your Mum's estate and passes automatically to your Father in it's entirety.
Your Father should be able to get some form of help from the social fund in the form of a crisis loan, but he would be well advised to seek the useful help of your local CAB who would help him by doing a lot of the work free on his behalf to alleviate the stress, and advise him exactly what help he is entitled to at this time of bereavement.
Speaking of which he may be entitled to a one off "bereavement benefit" payment, below. of £2000 tax free, besides other possible help with funeral expenses.
http://www.direct.gov.uk/en/MoneyTaxAndBenefits/BenefitsTaxCreditsAndOtherSupport/Bereaved/DG_10018703
http://www.citizensadvice.org.uk/cabdir.ihtml