Never send a Sig. Tell them to send YOU a sig. It has been known in unscrupulous circles for a sig to be copied onto an original document.
What lender is this first?
What do they need you to sign to continue an investigation? It either is or isn't. I it th CRA that wants you to sign someting or the OC (original creditor)? If the CRA (credit reportng agency) is requiring a signature, I would ask what for. Could they be setting you up to say you are trying to defraud the credit reporting agencies? Are they legit or invalid inquiies?