I figured, to having seen much of old Who episodes but just this discussion, that, as posters have stated, the Time Lords are locked in time and space. No one can get in to "save" them due to the lock, but there is little to stop them from trying to find a way out. a one way door. They're not dead, but the War continues behind the lock. But since no one can get in, they are effectively dead to everyone outside the lock.
They weren't erased from time, there's been a number of comments in NuWho about Gallifrey and the Time Lords being a legend or that they're all dead. Which means people do know about them and they existed at some point, known to the universeand not erased from existence.
I defer to those who have seen many of the episodes I have not.