Formal, somewhat archaic term for a lack of prudence or discretion, often used in written or historical contexts. Rare in modern conversation.
His imprudent remark made the problem worse.
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.
thoughtless person; inconsiderate person
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.