In my understanding of contract law, only the signatories to a contract are bound thereby. First, there has to be a contract between the debt collector and you. Secondly, for anyone else to make a payment on that contract, they must be signatory to it. If the family member who sent the debt collector a payment did so without being a signatory to any contract, their action does not create a contract between you and any entity, nor does it enforce a contract between you and the debt collector. The only way a relative could do that would be to have power of attorney, and I doubt they have this.
Research the statute of limitations for your State. Ten years means that you are most likely past the statute of limitations, and this debt collector cannot sue for this debt. If this is the case, send them a letter demanding that they cease and desist from contacting you. Tell them that you will report them to the appropriate Federal agencies if they persist. Keep a copy of the letter, and send the letter to them via certified mail, return receipt requested.