The point of the vaults was to expose different populaces to different types of problems and events. If they put so much thought into this, Vault-Tec is almost definitely still around. Not in the corporate sense that you may think though. I would guess that there is a group of scientists somewhere looking over all the data and everything and monitoring the progress of vaults and such. Perhaps it was even scientists from Big MT. Or they could be residing in what used to be MIT. Either way, there still must be some way that even a few scientists are still around and keeping tabs on the vaults.