On The Brink
On The Verge, Just In Front Of, Just Before
noun, suffix
Before you take the last measurement, you know you're on the brink of something.
すんぜん
This is a jukugo word, which usually means on'yomi readings from the kanji. As long as you know the readings for these kanji, you should be able to read this word just fine.
私の会社は破産寸前である。
My company is on the verge of bankruptcy.