Cathode to anode shorts are very very rare, and the sort of thing that should blow a fuse without damaging anything else. If not, the manufacturer has not thought things through.
I leave tube equipment on all the time. However, its tube equipment that I know is designed to not get in trouble if a tube fails. No blown cathode resistors, maybe a blown fuse. But in truth I have yet to have that happen despite using such amplifiers for over 35 years.
That's not to say that all amps are safe like that. The Fourier amplifiers mentioned earlier were prone to spectacular failures as were certain ARCs (when they were sold a bad batch of Cornell Dublier filter caps back in the 1980s).