'unethically-run' originates from English, composed of the adverb 'unethically' (un- + 'ethical') and the past-participle/adjectival use of 'run'. The prefix 'un-' meant 'not', 'ethical' traces to Greek 'ethikos' via Latin/Old French meaning 'pertaining to character or morals', and 'run' comes from Old English 'rinnan'/'runnan' meaning 'to flow, run, move'.

'unethical' developed from 'ethical' (from Greek 'ethikos' through Latin/French) with the negative prefix 'un-'; 'run' evolved from Old English 'rinnan'/'runnan' into modern English 'run'. The compound adjective form (often hyphenated) is a modern English formation combining an adverb + past participle/adjectival 'run' (earlier written as 'unethically run' without a hyphen).

Initially, elements had broader or different senses ('ethikos' referred to character; 'run' had senses like 'to flow' or 'to move'). Over time 'ethical' narrowed to 'relating to morals' and 'run' gained the sense 'to operate/manage' in contexts like 'run a business', yielding the current meaning 'operated immorally.'