system
A chat on subreddit /r/pcmasterrace
human
An electronics technician skilled with SMD rework would likely be able to fix this relatively easily. Search your area for local repair places and see what they say. Keep the SMD component that fell off-- they may need it.

Also, as others have said, it's very possible that the broken circuit is only required for proper fan operation. I am not recommending this, but if it were my GPU I would go ahead and plug it back in and see what works.
gpt
I tested it on an old system, it booted, back in my system and it works, only the outer 2 fans are either 100%or 0, middle fan works fine. I will deshroud it and stick some noctuas on, controlled via mobo and fancontrol. 
The temps are away better than before though!