Matthew, sadly I've gotten used to problem solving on the day off. That rarely phases me anymore.
Kiwitech, thanks for your post, it was helpful. We moved another musician to fill the empty chair and played one short.
Truly, this wasn't a big deal, everything was dealt with quickly, mostly due to the conversations on the music side of things that happened without me, there were very few things left for me to do. Worst case scenario, had I not been informed: start of show would have been a little delayed as I waited for a non-existent person to arrive front of house and had an ASM go looking for them (I can't start until all musicians are by the pit since they have to enter via the house), sound would have done a little scrambling adjusting the levels of the continuo in the stage monitors, the cast would have wondered what happened to the missing person (it's a very close group), there would have been an unattractive empty chair, stand and light at the edge of the stage. All things that can easily be coped with, but better to do ahead of time.
I have assisted on operas with normal sized pits where we've begun without a player - but normally that is because they can enter the pit unobtrusively, have another chair to play that part, don't play until late in the show, etc. and no one's been the wiser for it.