ずに済(す)むGet by without doing something, To get away with

ずに済(す)む is a grammar construction used in Japanese to indicate that one can 'get away without doing (A)', or 'it's no problem without (A)'. This structure is just a mix of ず, a literary auxiliary verb that attaches to verbs in the same way as ない (and has the same meaning), に, and 済(す)む, a う-Verb meaning 'to come to pass', or 'to end up'. Literally, it can be thought of as meaning 'it will work out without (A)'.

As mentioned, ず connects to verbs in the same way as ない, so this structure will be seen after the verbs that they are negating.

As the primary element in this grammar point that controls the meaning is 済(す)む, other negations such as ないですむ, or なしですむ may also be seen. 無(な)しで functions as a suffix, so may be used directly after nouns, unlike ないで and ずに.

In most cases, (A) will be something that is thought of as unpleasant or bothersome, therefore highlighting the speaker's relief that it can be avoided.