In every jurisdiction that I know of, it's illegal to install a larger breaker than what the wiring and outlets are designed for for exactly that reason.
Depending on where you live, there is a very specific exception to this in the US for manual welding machinery. You have to look for specific details in the code, but the conductors can be sized for 50-70% of the equipment's rated draw. This is also coupled with labeling requirements and a requirement to downsize the breaker if any other use is allowed on the circuit. This generally only applies to larger equipment. Typically, a 100A breaker for a welder could use #6 instead of the usual #4 or #2 (depending on wire, insulation and temp rise).
Something like a plasma cutter is generally too small to bother with this. I run mine off a standard 240V 30A line with #10 conductors.
Something must be going around, my plasma cutter died the other day. It's waiting for me to open up and check it out.