The definition of on the brink of is:
(idiom) about to experience something negative
The US economy is on the brink of a recession.
My son is on the brink of getting forced to leave his university because his grades are bad.
The criminal is on the brink of getting sent to jail, because he has committed many crimes.
Certain species of whales are on the brink of extinction because of whaling.
CNBC News – On The Brink
….on the brink of bankruptcy….