If a pin is bent, it is possible to repair, but it is very tricky since they are so small. I was able to use a sharp X-acto knife with a magnifying glass (and good light) to carefully push a pin back into shape.
If a pin is broken off, there might be hope, depending upon what pin it was. If it was a power or ground pin, then the system may still work fine without it, since there are redundancies for those. If it was a pin for a DIMM slot (LGA1156 or LGA1366, not LGA775), then you'll be okay as long as you don't use the associated slot.
However, if it's a critical pin, then the odds are poorer. If there's a bit of pin remaining, then it's theoretically possible to take a pin off from a trashed socket and attach it to what remains with a conductive adhesive (or possibly just wedging it in). But this is speculation on my part.
If you're really lucky, or you can afford it, you can find someone with a professional hot air or infrared rework station. The entire socket can be removed, the board cleaned, and a new socket installed. This is typically cost prohibitive to do on consumer equipment like PC motherboards, unless the motherboard is really high-end.