Yikes. I've seen them got hot enough to melt but not like that.
It may have just been a corroded connection right there. A lot of current goes through it (up to 20A), not enough to trip the fuse, but could generate enough heat to melt the plastic.

I think you can take the wire off the back, splice an inline fuse into it (like a stereo fuse, but the wire needs to be as large as the original). Just make sure to put the right fuse in (20A, not 25 or 30).