'irresponsibly-managed' originates from Modern English, specifically a compound of the adverb 'irresponsibly' (formed from the negative prefix 'ir-' + 'responsible') and the past participle 'managed' of the verb 'manage'.

'irresponsible' comes from 'responsible' (from Old French responsable, ultimately from Latin 'respondere' meaning 'to answer') with the negative prefix 'ir-' (from Latin 'in-' via assimilation). 'Manage' derives from Italian 'maneggiare' (to handle, from mano 'hand' < Latin 'manus') and Old French forms (e.g. mesnager), becoming English 'manage' in Middle English; the participle 'managed' is the past/past-participle form. These elements combined in Modern English into adjectival compounds like 'irresponsibly-managed' to describe the manner of management.

Initially the components referred to 'not taking responsibility' (ir- + responsible) and 'to handle or control by hand' (manage). Over time the compound came to mean specifically 'handled or run without due responsibility or proper oversight.'