Hello, Taylor. I am so very sorry that you lost your bird, especially when there had been no warning signs.
To determine exactly why your bird died, your avian vet would have had to perform a necropsy very shortly after she died. None of us are able to tell you, sight unseen, why she died, so there's no way, really, for us to advise you on what to do to protect the other birds. You really need to talk to your vet about this situation. If she was egg-bound, that would be something that would not affect the other birds anyway, unless an infection was present.
I would suggest that you double check the birds' environment: is it really big enough for 6 finches, some of which are nesting perhaps; do you keep it fresh and clean every day? How about their diet? Do you include fresh veggies and a bit of fruit, in addition to their seeds/pellets? Is their water always clean and plentiful? Do they get some natural light while being protected from too much? Do they get 10 - 12 hours of uninterrupted sleep each night? Are they all compatible? Discuss these things with your vet and perhaps it will give him/her some clues.
Again, I'm sorry for your loss. Good luck with the rest of your finches.