My friend has it (my choice of words in the first post is bad, I ment 'I came across') and as idiotic I was, I didn't take a photograph of it. I am currently unable to photograph it but I will do that when I get a chance. But it looks exactly like a pointy hat turned upside-down.
The case had Lastolite written in it and I tried to search their site unsuccessfully. Maybe some old model? However, the 'pointy hat thingy' had darkened marks that looked exactly like burn marks when lamps comes too close/stays too long too close to a silk (the marks where near the "mouth of the hat"), therefore I figured it must have something to do with lighting. Weird thing is, the wide side ("mouth of the hat") does not have any clips etc. with what you could attach it to somewhere or attach something to it. It is like a reflector (except instead of even, for example, silver surface, it opens up like a hat). I'm puzzled.
<- super neat illustration insted of a photo