without permission; without asking
Used when someone does something without obtaining prior consent or without giving notice. Often appears in negative contexts or as a set phrase.
He used my computer without asking.
It's rude to be absent without notice.
断る means 'to refuse' or 'to give notice/ask permission', and 断らず is its negative continuative form meaning 'without asking/refusing', so learners must track which sense of 断る is active.
Negative continuative form of the verb 断る (ことわる, 'to refuse; to ask permission; to give notice'). Literally 'without refusing/asking/notifying', it has become a set expression meaning 'without permission'.