Sometimes they do noting when connected backwards. I found one that had been through production testing & 72 hour burn in without shorting or exploding. Something else on that board had failed, and I spotted the backwards tantalum and replaced it.
As far as failed tantalums in repair: Tantalums lasted a hell of a lot longer than aluminum in the broadcast gear I maintained. The station had bought used Vital Industries Squeeze Zoom, and the matching video switcher. Thousands of caps had been replaced by the previous owner who had shotgunned them with aluminum, instead of the tantalum it was designed with. I had to replace about 100 a month with tantalums, till they were all gone. I liked that there was a small choke in front of every tantalum to limit the dV/dT. They also helped isolate sensitive analog sections from each other.