na-adjective, noun
Formal, somewhat archaic term for a lack of prudence or discretion, often used in written or historical contexts. Rare in modern conversation.
彼の不所存な発言が問題を大きくした。
His imprudent remark made the problem worse.
不所存の至りで、深くお詫び申し上げます。
I deeply apologize for my indiscretion.
無分別 also means 'indiscretion' or 'imprudence', but is more widely used and less formal than 不所存.
Compound of 不 (fu, 'not') and 所存 (shozon, 'one's opinion' or 'intention'), literally meaning 'not one's intention' or 'unintended', which extended to 'imprudent' or 'indiscreet'. The exact historical derivation is uncertain.