My Skutt kiln was plugged into the socket (240 volts). When I came in to check the kiln, the plug was completely melted. I was told the unit had not been turned on. Is this possible?
If there is current leakage between pins of the plug, almost a short circuit, then that can happen. Turning the unit on only conducts current to the rest of the unit inside its container.
If the current leakage between the pins was higher, you would blow a fuse. You need to check the fuse, or circuit breaker, for the circuit it's plugged into because it might be too large and allowed the plug to melt.
Of course, it sounds like there is a problem with the plug itself.
It's far more likely to burn up a plug during operation. The two conductors are well insulated from each other within the plug, often compartmentalied on heavier plugs. Thermal damage reduces conductivity and increases resistance. If while off, there would have to be a Lee Harvey Oswald "magic bullet" short between the poles - not too thick or it would trip the breaker, but still thick enough to do serious damage before its increasing resistance self-extinguishes, e.g. by burning up the shorting path. If while on, a loose connection on either conductor would suffice. Current is being forced through the connection by the electrical load, so the increasing resistance of the failing connection would make more heat, not less, creating a death spiral of increasing heat. The latter seems the more likely scenario, but an autopsy of the plug will tell the tale.
Was the plug recently replaced? Stranded wire strands can get away from you, and lay a single strand or two where they should not be. But it would fail shortly after plug replacement. With a pre-manufactured plug with a molded end, that is improbable. That's why I like those.
And how would an operator be reasonably expected to notice? It's a kiln. It produces lots of heat and smell, which would tend to mask the problem.
It's possible the crew is telling you it happened after it's off, merely to CYA. It's possible they didn't know. Is the plug on your PC plugged in all the way? Of course, CYA presumes that the worker would have had any ability to prevent this. I doubt they could. Maybe someone yanked really hard on the cord, maybe not the worker, but that's on the employer, workspaces must be set up so trip hazards are avoided and cordage is protected. Maybe they're just worried about a boss who is a bit irrational sometimes.
In most instances of a plug melting on a heavy current device, such as a kiln, it is due to a poor connection. That could be the electrical outlet contacts not grabbing firmly to the contacts on the cord when plugged into the outlet. But it could also be due to a loose connection in the plug itself. Current flowing through the poor connection can create heat at high enough temperatures to melt the plug or even the outlet itself. This would normally happen when the kiln was in operation and could have gone unnoticed during the previous usage cycle.
The style of cord assembly shown as a replacement for a typical Skutt 240V Kiln at the company web site in the Portland area shows that the plug end is an assembled unit that most likely uses screw terminal connections to secure the wires inside. This type has a greater chance of developing an a poor connection inside than a molded plug assembly where the wires are crimped or flash welded to the contacts.
It is possible that another type of failure could create a short in the plug assembly or in the wire cable right near where it exits from the plug assembly. Such short can also create high heat and melt the plug but this would almost always result in the the circuit breaker opening at the power panel at the facility. If the kiln had been previously used and then the plug melting occurred after the fact then it would imply that the shorts occurred when the plug was simply left plugged in and undisturbed. I suggest that this is unlikely due to the fact that an intermittent short is more likely to occur when the cord or plug is flexed or moved around.