Mineral Deed - Successors and Assigns

I need to know on a mineral lease what ( her successors and assigns forever ) . Does this mean that all rights for any member of the two families on the lease have no claim and the lease is free and clear.

This question is too vague. Are you asking about the language in a deed or in an oil & gas lease? What percentage did grantor own? What state are the interests in? You need to post all the facts such number of parties to deed and/or lease, how you or other party is claiming rights, etc.

My mother purchased is lease in a bankruptcy in 1979. In the filing it states that any rights are given up for her successors and assigns forever this lease to the 3rd party my mother.
I am assuming that we own the lease out right and any relatives of the lease we bought have no interest anymore.

Please read response to above

It depends on who was in bankruptcy to determine exactly what your mother acquired. As you know, the lease has 2 parties - mineral owner as lessor and oil company as lessee. Over time, both the mineral rights (lessor) and the leasehold rights (oil company) may be assigned in whole or in part. First question is whether the mineral owner or oil company was in bankruptcy. If it was the oil company, then your mother acquired the leasehold rights which were a working interest in any oil wells and right to drill and develop with respect to the leased minerals. Then you need to determine if the leasehold rights were depth-severed so that she only had a right to specific depth(s). She would also have liability for plugging the wells. If all the wells have ceased producing in the intervening years, then her leasehold rights will have terminated. It is possible that the leasehold rights are being kept alive by producing wells in formations which were severed. If the mineral owner was in bankruptcy, then you need to research to determine what he owned at the time of the bankruptcy. But then your mother should have gotten a deed to the minerals. It depends on state law and the bankruptcy court. You may want to have an attorney review the associated legal documents to help you figure out what your mother acquired.

This was a non producing lease , just the mineral rights. There were just two parties involved my mom and the mineral rights owner.