Unless this is joint credit that both your Father and Mother has signed up for, then the debt is forgiven upon death. If all she is an authorized signer, then she is not legally responsible for the debt nor would she no longer be able to use the account. And since Allied Collections refuses to provide you valid proof that your Mother is liable for this debt, then she owes nothing and should pay nothing.
The next time Allied Collections calls, tell them that unless they send your Mother valid proof that she owes the debt, then you tell them that you no longer wish to have them call you about this matter and that any further harassment regarding this will be reported to the Federal Trade Commission and you will be seeking a lawsuit. Also send them a Certified Letter - Return Receipt requested to show proof that your Mother asked for valid proof regarding the debt.
Also check with your State Attorney General to see how collection laws are governed in your state to see what her rights are in this matter. Hope this helps you.
Sincerely,
Anonymous Individual - Three Rivers, MI