I recently had a 15A receptacle in my kitchen partially melt while my wife had our vacuum cleaner plugged into it.
We knew something was up when we smelled the telltale hot plastic smell. I felt the wall-plate and it was hot. I turned off the breaker, took everything apart, and found that the outlet was being used as a pass-through to power two of the counter-top outlets in our kitchen and our very large kitchen refrigerator/freezer.
Supposedly even a 15A outlet is rated for 20A pass-through, but something wasn't right if it melted, so I went and found a replacement duplex outlet, some #14 wire, and re-wired it using pigtails so the outlet wasn't passing through any current.
I wrongly assumed that the circuit was 15A. When I went back to turn on the breaker, I discovered that it was a 20A circuit. Uh oh. My pigtails were under-rated for the circuit.
I also used a take-out receptacle that I had lying around, and it was ivory rather than white.
I told my wife not to plug 2 heavy-duty loads into that outlet until the weekend, and today went out and bought a new white duplex receptacle, found some #12 Romex from which I could cut new pigtails, and rewired it properly, both with the correctly colored receptacle, and with the proper gauge of wire.
I got to thinking, though. Resistance is measured in ohms per foot. A 14 gauge wire carrying a 20 amp load introduces too much resistance over the length of the wire run, causing a significant voltage drop and heating up the wiring and risking a fire.
However, a pigtail is typically less than 4 inches long. I'm not advocating it, but couldn't you use 14-gauge wire for such a short piece of wire and not generate enough of a voltage drop to cause a problem, even if you were to plug 2 devices into the receptacle that drew a total of 20 amps? (Again, I understand that that would be a violation of code, and I'm not about to do it in my house. This is a theoretical question.)