せずにすんだ

managed to get through without doing or experiencing something

→ 為る
phrase Rare #34,517
managed to get through without doing or experiencing something Used to say that someone fortunately avoided an undesirable action or outcome. The form せずにすんだ means that it ended up being unnecessary or was avoided.
JA: 幸い、怪我をせずにすんだ。
EN: Fortunately, I got away without being injured.

そのようにして彼は事故でけがをせずにすんだ。

That way, he avoided getting injured in the accident.

幸い、怪我をせずにすんだ。

Fortunately, I escaped without getting injured.

幸いにもけがをせずにすんだ。

Fortunately, I escaped without getting hurt.

会社は何とか倒産せずにすんだ。

The company somehow managed to avoid going bankrupt.