With solid state amps, the most common cause of problems like you reported would be accidentally shorting out the amp by touching the two speaker lugs together. That sort of problem will usually mean just a blown fuse. Only a very poorly designed amp would not have protection from such a common accident as that one.
With tube amps, there would be no problem with a short of this type. While people often talk about tube amps being prone to failure from a speaker wire being disconnected, that really only happens if the amps were being played very hard and the disconnection were for a long period of time. Even then, I have never heard of an amp actually failing from this theoretically problematic condition.
It is a good practice when doing ANY sort of work connecting and disconnecting wires--speaker wires or interconnects--to have the amplifier turned off. This prevents any sort of problems with shorts or loud pops coursing through the system.