I am looking at acquiring the rights to a book published in the UK in 1982. The book is out of print and the publisher no longer exists. I understand that another company might have bought the rights if the publisher sold. But, what happens if it ceased activity because it was a small family business and the owner died? Do the heirs now own these rights?

Also, the daughter of the book’s author says she paid the publisher to have the book published, but no longer has record of any contract.
The small prints say that permission to use material must be given by publisher.

What is the course of action for both the daughter who is willing to grant the rights, and myself who is willing to acquire them?
Thanks.