The cap binds the signatory, and only the signatory
A liability cap in an engagement letter is a contractual term between you and your client. It has no effect on somebody who never signed it. A client's business partner, an investor, a competitor or another third party can bring a claim about the same advice and arrive unburdened by the number you negotiated. That is why limits on this cover are sized to the loss a claim could represent rather than to the cap you agreed, and firms that size to the cap are the ones most surprised.