You may be right about Dropsync being the culprit, Morland. Upon further investigation, I see that Dropsync (the Pro version) on the tablet says that 657 files have been deleted this morning.

I realized that a third computer (a laptop) had sync'ed with Dropbox just two days ago but not since, so I've copied all its Dropbox files onto a thumb drive for safe-keeping.

It looks as if everything will be recoverable, but not without some time investment.