Excessive current draw
The socket looks like others I've seen where the bulb has slowly gone bad and has caused an excessive current draw or resistance in the filiment causing the bulb end to get excessively hot causing the melt down you show.
"Tell me and I will listen, Teach me and I will learn, Show me and I will accomplish, Involve me and I will succeed."
'84 300SD 256,000 Gold on Brown (Mileage Award)
'86 300E 246,000 Blue on Tan