No, he is not responsible for her debts. Some years ago I helped an elderly man whose wife died leaving huge catalogue debts. She left no estate and he could not be made to pay his wife's debts because the company's contract was with his wife not with him.
The companies will always chase partners and spouses, to see if they will pay because, not unreasonably, they want goods they supply to be paid for, and in many cases, families have the means to do so and do so willingly. But legally these companies are up the creek without a paddle and cannot force her partner to pay the debts
The only problem that could arise is if your DD opened the account in her partners name and the company understood that they were doing business with him, not your DD. If that has happened it is possible he was unaware of it, but if he knew, then he has to pay.
However there is no point in these firms chasing someone who has no assets and is unlikely to have any in the forseeable future so, if the accounts are in his name, he should get CAB to write a letter pointing this out and asking them to cease chasing him. His credit rating will take a hit, but that cannot be avoided.
However if the account is in DD's name, 'with one leap he is free', although it may take a letter from CAB to these firms to poiint that out.