ずに済む|ずにすむ

Expresses that one gets by without having to do something that would otherwise have been necessary or unpleasant, often because of favorable circumstances or preparation. It carries a nuance of relief.

Used in both conversation and writing, very often in the past tense (ずに済んだ) to report that something troublesome, such as spending money or waiting, turned out to be unnecessary. The reason is typically stated in a preceding clause with ので or から. Unlike ざるを得ない, which expresses being forced to act, ずに済む expresses being spared from acting.

• なくてもいいN4「なくてもいい」 means it's okay not to do something, expressing permission or exemption from an obligation; it can also mean it's fine to lack something or not be in a certain state. 「ずに済む」 emphasizes that a burden was actually avoided as a result of some reason, often with 「ずに済んだ」 to express relief, so the two are not interchangeable.
• ことはないN3「ことはない」 attaches to the dictionary form and is mostly used to comfort someone with 'there's no need to...'. 「ずに済む」 states that a burden was avoided as a result of some reason, often with 「ずに済んだ」 to express relief. They are generally not interchangeable.
• ざるを得ないN2「ざるを得ない」 means the opposite: being forced by circumstances to do something, or having no choice but to judge that way. 「ずに済む」 means a burden was avoided as a result. Both take the same conjugation (する becomes 「せ」 in both), but 「ざるを得ない」 is more formal and stiff in tone; they cannot be swapped.
• ずにはいられないN3Both take the same conjugation, but their meanings point in opposite directions: 「ずにはいられない」 means being driven by emotion or impulse and unable to resist doing something, while 「ずに済む」 means that, for some reason, you end up not having to do what would otherwise have been a burden. They cannot be swapped.
• ずにN3「ずに」 links two actions within a sentence, meaning 'without doing...' or 'not doing... and instead...', and by itself carries no sense of a burden being lifted. 「ずに済む」 means you end up not having to do something, with a sense of relief, so the two cannot be swapped.
• に越したことはないN2「に越したことはない」 states the general principle that 'it's naturally best to...', and can attach to verbs, adjectives, and nouns. 「ずに済む」 attaches only to verbs and says that a burden you would have had to bear ends up being avoided, often with a sense of relief. The two cannot be swapped.

Unlike なくてもいい and ことはない, which state that something is not necessary (as permission or advice), ずに済む reports relief at being spared from it, and ずに alone just means 'without doing.' It is the opposite of ざるを得ない (forced to do) and differs from ずにはいられない (can't help doing) and に越したことはない (it's best to do).