liableyoudaoicibaDictYouDict[liable 词源字典]
liable: [15] Today’s main meaning of liable, ‘likely to’, is a comparatively recent development. Its primary sense is ‘legally bound or obliged’ (as in ‘liable for someone else’s debts’), which goes right back to the word’s ultimate source, Latin ligāre ‘tie’. Its Old French descendant lier is assumed to have give rise to an Anglo-Norman derivative *liable, literally ‘bindable’, which English took over.

Other English words that come ultimately from ligāre include ally, liaison [17], lien [16] (etymologically a ‘bond’), ligament [14], ligature [14], oblige, religion, and rely.
=> ally, liaison, lien, ligament, ligature, oblige, religion, rely[liable etymology, liable origin, 英语词源]
liable (adj.)youdaoicibaDictYouDict
mid-15c., "bound or obliged by law," probably from Anglo-French *liable, from Old French lier "to bind, tie up, fasten, tether; bind by obligation," from Latin ligare "to bind, to tie" (see ligament). With -able. General sense of "exposed to" (something undesirable) is from 1590s. Incorrect use for "likely" is attested by 1886.