managed to avoid; got through without having toUsed to say that something undesirable was avoided or did not end up happening. せずに means “without doing,” and すんだ is the past form of 済む, indicating that the situation was resolved without doing it. The expression is often written as せずに済んだ.
JA: 幸い、怪我をせずにすんだ。
EN: Fortunately, I managed to avoid getting injured.