There is no "statute of limitations" for reporting a felony conviction on a job application. Your son's conviction is a public record and he could be fired if he fails to disclose it in response to a question on a job application... even years later, if they didn't find out about it in the first place.
Unfortunately, since your son served prison time, he is not eligible for dismissal under Penal Code §1203.4 (commonly called an "expungement") or reduction of his felony to a misdemeanor under Penal Code §17(b).
I think your son confused the time period during which a prior DUI can be used to increase the punishment of a new DUI conviction. In 2002, it was seven years, but it has been increased to ten years since then. It will also stay on his DMV record for ten years.
Note that ANY DUI conviction within ten years of a felony DUI conviction can be charged as a felony.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
I'm not sure what the PO was referring to with respect to the "statute of limitations." Statutes of limitation generally operate to bar the filing of stale allegations. Very likely, there was a miscommunication and that the seven years referred to the (then) length of time the convictions could be charged as priors to enhance punishment for any future DUI. That length of time has been increased to ten years.
I would be wary of failing to report a felony conviction to a prospective employer. If the employer does a background check, the felony may be revealed and the deception would justify either not hiring your son, or firing him if it is discovered after he is employed.
It is not correct to state that it is impossible to clean up your son's record. Although he has been to prison, he should consider petitioning the court for a certificate of rehabilitation. Without knowing the facts of the underlying convictions he has suffered, or what your son has been doing since his release from state prison, it is not possible to assess the merit of a possible petition. I would recommend that you talk to an attorney experienced with post-conviction relief who can help your son with this or, at the very least, to begin advising him on what he can be doing now to increase his chances of cleaning this up in the future.