A keen, razor-like edge; hence, any situation which is precarious and close to the verge of destruction: as, to stand on the razor-edge or razor's edge.(noun)
The Century Dictionary (Public Domain)
Use "razor-edge" in a sentence
"I frequented bars, stayed razor-edge thin, and was sort-of although I could be mistaken dating a drummer from a band called Otis Coyote."
"He drew it forth - it was fully two feet long -- and, to demonstrate its razor-edge, sliced a sheet of newspaper into many ribbons."
"The blade of the hatchet had been ground to razor-edge."