a situation when you are almost in a new situation, usually a bad one
on the brink of death/disaster/war etc
In October 1962 the world seemed on the brink of nuclear war.
The company had huge debts and was on the brink of collapse.
to the brink (of something)
managers who have taken their companies to the brink of disaster
back from the brink (of something)
He will go down in history as the leader who pulled us back from the brink (=saved us from disaster).
to make someone start doing crazy or extreme things
the edge of a very high place such as a cliff