Attaches to the negative stem (nai-stem) of verbs; for サ変 verbs, use せずに. Expresses that an action is not performed while another action occurs. Often interchangeable with ないで, but ずに is slightly more formal or literary.
See also: ないで
I went to school without eating breakfast.
He left the room without saying anything.
It's impossible to take the exam without studying.
Derived from the classical negative auxiliary ず combined with the particle に, forming an adverbial phrase meaning 'without doing'. The form is a remnant of older Japanese grammar still used in modern written and formal speech.