Usage patterns
〈事〉の淵に沈むto sink into the depths of (despair, sorrow, etc.)
He had sunk into the depths of despair.
〈場所〉の淵に落ちるto fall into a deep pool
He fell into a deep pool in the river and nearly drowned.
死の淵をのぞくto come to the brink of death
He suffered a serious illness and came close to death's door.