Person A (Wife), with Person B (husband), refinanced their house prior to filing for divorce. Person B promised Person A, a portion of the money earned from the refinancing, to help her get a new place. In return, Person A signed a "QuickClaim Deed" for Person B to have the refinanced house to himself. In filing for divorce, both parties stated that what was Person A's stuff is hers and Person B's stuff was his. All debts from that point forward, were each persons (A debts is hers and not B's / B's his and not hers). Now Person B wants to sell the house and asked Person A to sign papers for permission. Person A wanted to know why and Person B said she was still on the mortagage. Person A is now concerned of her libility to the old property (Person B has stated they may file for bankrupct). Person A is also concerned of what creditors could have rights to regarding her new place or any of her current assets.

So if I understand correctly: the wife signed a deed to the husband. He then refinanced the home and all debts owing on the home were paid off and the wife received a portion of the net due at closing. If this is correct, she shouldn't be on the mortgage if he signed it solely without her.
Who told the husband she is still on the mortgage? Sounds like somebody has made a mistake.

If he actually refianced then she is not on the mortgage, if he merely agreed to finace but never did, she is still on the mortgage.

I see you said B promised A portion of the money at refinacing, but I don't see you saying they were ever paid.

If the original mortgage is still valid, then yes she is liable to the mortgage company, she can sue husband if he would default, because of agreement in divorce court. But the ruling of divorce court does not void the original mortgage, but would merely order them to get a new loan.

If B filed for bankruptcy and did not pay the mortgage, and the orgainal mortgage is still in place, they will come after A for the money.