Residential electrical sockets are not very complicated. Inside the plastic casing are metal clamps designed to hold a plug, and these are connected to the terminal screws on the sides. When the power is on, an outlet can't discharge electricity until a plug is fully seated in the clamps. Occasionally a loose connection or defective wiring may cause arcing or overheated metal, and this in turn may cause the plastic casing to melt.
Anatomy of an Outlet
The plastic faceplate of an electrical socket is called the receptacle. The spring-loaded clamps designed to hold the plug sit directly behind the slots in the plastic, and they connect to the terminal screws. Manufacturers don't design outlets to be taken apart, so a permanent layer of plastic encases the clamps and their connections. There are two terminal screws on each side, brass on one side and silver on the other, and a green ground screw on the bottom. The brass terminals are for hot leads and the silver ones for neutral.
When electricity jumps across a gap between two conductors and creates a spark, the phenomenon is called arcing. As the electricity ionises the air to produce the spark, it produces heat at the same time. Arcing near an electric outlet can create enough heat to melt the plastic. It can be caused by a loose connection on one of the hot terminal screws, by a poor connection inside the outlet or by a loose clamp that doesn't hold the plug securely enough. Outlet clamps wear out, given enough time, or they can be loosened when plugs are pulled out often and carelessly.
Every conductor has some resistance to electricity, and this resistance increases as the wire diameter decreases. Since resistance produces heat, a smaller wire carrying electricity of a given voltage and current will heat up faster than a larger one. If the wires supplying an outlet are too small for the load, the terminals can heat up enough to melt the plastic faceplate. Similarly, if an extension cord is too small for the load it supplies, the plug prongs can heat up enough to melt plastic.
If an outlet supplies an appliance or tool that needs extra power to start, such as an air conditioner or circular saw, the power surge can generate enough heat to melt the plastic around the prongs. This is more likely to happen if the extension cord isn't sized correctly. Similarly, a sudden ground fault caused by exposed wires in contact with water can send a surge through the prongs, as can a short circuit caused by the wires touching each other. The circuit breaker controlling the circuit will probably trip, but the surge can still produce enough heat to melt the outlet.