You are correct written contract statute of limitation is 4 years in California. You can send them a cease and desist letter as well. Here is some information that might be helpful.
I am not sure if your pay day loan required you to sign a form or other contract setting forth terms and conditions. If you made any installment payments, then a suit might be for 4 years after the last payment. If in continuing doubt you should show all your paperwork to a local attorney.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
The statute of limitations in California is four years from breach or from the last payment, whichever is later.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.
Unless they obtained a default judgment against you, the statute of limitations is, at most, 4 years from date when the last payment was due or was made. Because they are offering such a discount, it is doubtful that they have a valid claim. I advise that you do not waste your time talking with them. You will just get aggravated and you might accidently say something to revive the Statute of Limitations. If you fee that you must respond to them, have your attorney ask for a copy of all of their documents and a computation of the amount owing. This is called "validation". This is different from "verification."