Tub re-glazed and re-caulked, drippy residue from caulking
I have seen this happen just once before - a caulk that never seemed to cure. It just stayed runny, even when given multiple days to do so at room temperature. My guess is the caulk was old or stored under conditions that caused it to fail to cure, or perhaps it was simply a bad batch from the manufacturer. Regardless of the reason, clean it out, and redo the caulking job.