Is a 2011 MacBook Pro VGA card fixable?

It is fixable but I don’t think it’s possible to get it repaired at Apple Store because it’s considered as a vintage product. However, you can get it fixed at an Apple authorized repair provider. First you’ll need to know which graphics card your MacBook has: https://support.apple.com/en-us/HT202053

There is no separate graphic card on MacBook Pro 2011 models. so don't bother trying to find such a card on eBay -- there is no such card.

What are your symptoms, EXACTLY?

There may be some serious work-arounds that do not require parts.

I'm assuming you are referring to the known GPU issues with the 15" or 17" models? If so, it depends what you mean by "fix".

First, a 2011 Mac is no longer supported by Apple as it is considered "Obsolete" so Apple will not work on it and an AASP will not be able to get official parts for it, although some may be able to acquire a refurbished Logic Board (or have your board refurbished), but this would not be cheap and makes no sense spending that much money on an outdated model where the same problem could occur again.

Depending on the severity of the failure and how you use this laptop, then you may be able to disable the discrete GPU and use the Intel GPU instead, but you won't have the full features of the laptop. Sometimes you can use the gfxCardStatus app or if you cannot currently boot normally or into Safe Mode, then you can use the dosdude technique:

https://gfx.io/

https://github.com/steveschow/gfxCardStatus

http://dosdude1.com/gpudisable/

Cards and other components are not repaired, they are replaced.

The problem is your Mac is 11 years old and no longer supported by Apple. That means the supply of parts has likely dried up a long time ago.

You may find parts on places like eBay, but they're be used most likely and you never really known what condition that really are in. The question you need to ask yourself is how much time, money and effort are you willing to put into an obsolete Mac.

[Edited by Moderator]

Apple doesn’t fix video chipsets. In any case, it’s not VGA but either Intel’s integrated video plus perhaps another video chipset. It’s soldered to the logic board, and when Apple fixes it, the solution is at least a complete logic board swap.