Macbook Pro Late 2011 13" Display Issue
It sounds like there is some problem with the connecting wires for the display. If you're okay how things are, then you can just leave things be. A repair would probably cost several hundred dollars.

I have the same model Mac and also have display issues. When it was almost one year old, I noticed that the display would often go wonky (not turn off but look all weird like a light show), often if I were to open it all the way, if I recall. (So some problem with the internal wiring, probably different wires than yours though.) This was mainly a problem when I took it to class and was more prone to open the display all the way. So I quickly bought an extended warranty as someone from Apple predicted that my display issue would get worse and require a repair. But the issue never got worse, and I was always fine the way it was. I've been using this laptop for almost five years (still snappy!), and only very rarely do I experience this problem again, and the problem goes away by closing the lid and opening it more normally.