I agree with Spehro Pefhany. This happens when the wire is not tightly held down. When that happens, and current is being drawn through the circuit to power something, an arc can form where the connection is poor. That arc acts like a switch so current continues to flow.
However the arc will reach temperatures over 1,000C melting and burning things. Further, since metals expand when heated, the arc actually makes the connection looser so it can be a run-away condition.
That effect introduces a secondary cause. A badly fitting plug used in the outlet can cause arcing where the plug touches the internal connections. The heat caused by that will heat the whole thing and can loosen the screw making the situation worse. Result, smoke, acrid smell, and a hot plug. Unfortunately, this type of plug and socket technology is very old and cheap and, for the currents they are expected to carry, rather badly under-designed. Using even cheaper imported outlets exacerbates the problem.
As Sphero also mentions, it also looks like it got wet at sometime. If this is a basement it may have been flooded at some point. Anyhow, the rusting of the screw just makes the bad connection worse and more likely to arc. Another reason why not to install cheap outlets.
You, or the previous owner, are lucky the house did not burn down. I can't believe someone did not smell or even hear it.
And why only the white leads, not the live wire?
It's about current. It does not matter which wire is loose since whatever current flows out the live wire must return through the neutral.
It also looks like whomever wired that up used cheap outlets and was not a professional electrician. You should check them all and, if you can afford it, invest a few dollars and replace them all.