Do professors discuss about their PhD students or other PhD students and their performance or likelihood of being successful? Grad student community is much smaller than undergraduate community and often a professor has just handful of PhD students under them. So, it is possible the other professors might know about an underperforming or overachieving student from a different group.
If yes, what is the nature of discussions that they have? How often do they feel the need to advise or provide assistance to a student that might have caught their eye?