I've decided to accept the duplicate suggested by a few people as it's a bit more broad and is probably easier to apply to various real-life scenarios others might find themselves in. This particular question was created from a specific scenario that didn't even affect me, personally. I am, however, grateful for all the responses that were submitted.
Disclaimer: I'm asking this question on behalf of someone dear to me - I do not have all the information beyond the general situation.
My GF was very unhappy with her job - the pay was low and management was sort of a joke (note that "management" in this instance is her direct manager, not the company owner); she was denied bonuses (when everyone else got them) for example, probably because she received a small raise after she was responsible for successfully completing a VERY big project for a very important customer almost single-handedly. Finally the company has undergone some restructuring recently and now implements a corporation-like structure; all the red-tape with very little of the benefits because the employee count isn't that of a big corporation (for example the mentioned manager had literally only TWO people under her supervision).
She found a different job offer and passed the recruitment process and was sent a pre-contract to sign (standard 3-month trial period with the agreed upon salary). She hasn't yet signed it because she wanted to try and negotiate a shorter notice period with her current boss; if that'd go through this pre-contract could be changed to let her start the new job faster (and no real loss if this request would be denied).
Well, her boss was quite shocked that she wanted to leave, and came back with a counter offer. It seems he was quite impressed with her handling of the important project I mentioned earlier and agreed to not only match the pay-raise of the competition but raise it slightly. Supposedly he understands the "management problem", but the solution is that said manager will be assigned to another team...
This all seems a bit worrisome IMHO, and I wonder if this is a red-flag or not. Specifically, that her boss effectively doesn't know if his valued employees are happy or not. Additionally, the raise is 50%, so not an insignificant amount and it's only offered when threatened with the employee in question coming in with a letter or resignation.
While I fully understand that no one here can really make a decision for my GF, I am quite interested how often such a situation ends up in the employees favor (employee threatens to resign, gets significant raise, stays).