Found this while browsing Facebook. The halogen lamp melted to the point it sagged.

Glass halogen lamp operating at the tempreature of the quartz ones? (I can't view the picture, since it is on Facebook, and I don't plan to create an account there in order to save my anonymity and privacy).

I believe it's quartz, and I don't think you require an account to have a look. Although I am currently logged in when viewing it.

Wow, I haven't seen that happen before. I have seen the filament in linear halogens sag and melt through the quartz, though. If the lamp starts to blacken it will run hotter, so I guess this could happen.
We use a lot of 300 and 500 Watt halogens at work, and they usually just burn out. Some of the cheaper bulbs would crack or bulge, but I try to stay away from those. GE, Ushio, and Osram all seem decent. (I'm in 120 Volt land, by the way.)

Wow! That's melted! That happens with cheap chinese linear halogens

It is strange:
Normally the quartz melts within quite narrow temperature range, way narrower than I would expect for the heat uniformity along the lamp.
And the pressure inside of the lamp is usually higher than atmospheric (although not too much with modern Bromine based designs).
So the eventual overheating usually yields a kind of bubble formation - the point of highest temperature melts first, the inn er pressure blows a bubble from it.

This really looks like some material with wide transition range (temperature difference between softening and real melting into liquid), so definitely not quartz (or at least heavily contaminated) - it softens along the complete length just so it bends, but not enough to bulge (or collapse in case of below atmospheric pressure design).

Maybe DSWI installed the lamp without using a piece of tissue to clean the finger print oils off.

Here is the picture for people who are not on Facebook and want to see it

Maybe a reflector tht  reflected part of the light onto the lamp. As the lamp started to melt and sag, the first deformed sections moved out of the reflected focus and next sections moved in, so the melting point moved along the lamp to melt it slowly and relatively uniformly

Finger prints would make the lamp discolor or explode in the spots where it was touched, not uniformly along the entire lamp

Lamp isn't getting proper cooling?Looks like-wrong mount position and lamp overheated.

But if it would be clean quartz, when overheating due to any reason it will melt on one spot first and form a bubble there. Moreover the finger prints would more likely be localized, so again the bubble.

By the way it looks like a lamp with the IR reflective coating - maybe that turned from IR reflective (reheating the filament) to IR absorbing (so heating the tube wall instead of the filament) for some reason (could be wrong thickness, so a manufacture fault, or degradation by either heat, moisture or time, or combination of all)

I've replaced a couple of such bended Halogen lamps which were mostly installed in cheap fixtures. All of them were 1000W and 1500W.