Boxcar is correct.
From a practical point of view, consider obtaining an annual inspection from an IA. Six months later his examiner status expires, he makes no effort to renew it, and joins a nude sunbathing cult in Guyana. Is your annual inspection no longer valid? No, it's just fine. Further, that IA takes the responsibility for the inspection weather he keeps his inspector status current or not, and he retains that responsibility, as well as responsibility for all the work performed on that airplane up to the date he did the inspection. He retains this responsibility until the next annual is performed.
If an instructor makes an endorsement, and is an authorized instructor, then the endorsement is a done deal. Suppose I endorse a student today, but tomorrow I run into an intersection on my motorcycle and die. Is the endorsement no longer valid? Suppose it was a flight review? My currency has expired, but has his? No. That's not a very good exampe, though. Suppose my instructor certificate expires the next day, after the flight review, or endorsement for conventional gear, high performance, complex, or high altitude. Even in each of these cases, the endorsement is valid indefinitely, as it has never been issued an expiration. My certificate has an expiration, but not the endorsement.
I caught the short end of the stick on this one, some years ago. I was asked by a flying club to ride with an individual in a Cessna 172 for them. He was current in a 172, and was checked out in all the other airplanes in the club. I rode with him, he demonstrated his ability, and we landed. I made a notation in the club paperwork that he had completed the flight and demonstrated proficiency, and that was that. I made a notation in his logbook that we had flown, the maneuvers performed, the duration, the purpose and results, and signed it.
Several years later, this individual crashed an airplane. Coincidentally, it was the same airplane from the same club. He didn't have a current flight review, and had an expired medical certificate. He didn't have current 90 day flight experience, and he crashed doing a crosswind landing at a remote airstrip in terrain. Who do you suppose was the first person everybody (and their dog) came looking for? Me. I had insurance companies, the flying club, the FAA, and a dog, breathing down my neck (gotta say, I kind of liked the dog).
I even had a call from the manager of that club telling me that if I'd sign and backdate a flight review, he'd see what he could do about leaving me alone. I refused, and offered evidence from my own logs and records of what had been done, including my specific admonishment to that individual to keep current, maintain a current medical certificate, and keep a current flight review. Eventually I was left alone, but not without a headache.
By the time all this had happened, I had let my instructor certificate lapse...it wasn't current by any means. That didn't change the fact that mine was the last signature in his logbook. It made me very popular for a little while. Once you put your signature down, you're down, as they say.
This leads to another point of consideration. Many instructors feel that they can protect one certificate by signing with another. For example, by signing with a ground instructor certificate, they are protecting their flight instructor certificate if the student doesn't pass. Not so. All certificates are tied to the same individual; one gets called up, the others get called up. They're all on the same page when your record is called up, because it's the same record.
I hold five different FAA certificates. Certificate action on one may or may not lead to action on the others. For example, a violation for maintenance practices may affect my mechanic certificate, but not my pilot certificate. However, the FAA also has the option to suspend or revoke all my certification. Certain offenses are cause for suspension or revocation of all certificates.
I have five different certificate numbers. Using one number won't protect the other numbers. It would, if they were held by five different people, but enforcement action is taken against an individual, rather than against a certificate. If you're a mechanic, you risk your pilot certificate when performing maintenance. Many don't realize this. If you're an instructor, you risk your pilot certificate when instructing...even when you're not acting as a pilot. And so on.
As a cockeyed example: While taxiing your DC-3 past a group of co-workers, you elect to hang your bare butt out the window to salute them. Your ATP certificate is suspended (careless and reckless operation), and action is taken on other certificates in your posession as well (lack of moral character). Lest this appear farfetched, it happened a few years ago. The moral character clause was the main impetus to revoke the airman certificate, and this applied equally to other certification. The reasoning being that one who is not mature and competent to hold a pilot certificate should not be entrusted as an instructor or engineer or mechanic...etc. It does happen.
The best bet is to withold your signature until you are confident it's well founded. Be sure the student will pass, won't crash, bathes daily, chews his or her vegetables at least 40 times before choking them down, and doesn't abuse small animals or children, except on Sundays. (The FAA doesn't work on Sundays, except when they do). My .02, now worth .01 and falling...