~ずに済む (get away without)
grammar4 sentences
The frame [verb-neg]+済む for 'getting away without having to X / managing without X-ing' — used when an unwanted action or obligation is avoided. Surfaces as ~ずに済む (with classical negative ず: 言わずにすませた, ぬれずにすんだ) or ~なくてもすむ / ~なくても済む (with modern なくても: 勉強しなくてもすむ). Same construction in different negative forms; ずに carries a slightly more elevated register.