If they don't have anything joint financial wise, then she should phone Equifax and find out how to go about removing her partner as a financial associate.Remember that credit records can vary and the information may be on more than one. She might also want to make enquiries with Experian and Call Credit as well.
In regard to a mortgage application, this could still be affected by a partner who has been in financial difficulty. If he had loads of debts, CCJ's or any bankruptcy/insolvency issues, mortgage underwriters may see this as a risk. It is not about the house, as he has no interest in that, but your daughter could have difficulty repaying the mortgage, if she felt obliged to help him with his debts.
I am not an expert on mortgage underwriting, but having worked in financial services, I have come into contact with such issues. There are a couple of independent mortgage brokers who post to this site, so they may have a more expert opinion.