loose (adj.)
early 13c., "not securely fixed;" c.1300, "unbound," from Old Norse lauss "loose, free, vacant, dissolute," cognate with Old English leas "devoid of, false, feigned, incorrect," from Proto-Germanic *lausaz (cognates: Danish løs "loose, untied," Swedish lös "loose, movable, detached," Middle Dutch, German los "loose, free," Gothic laus "empty, vain"), from PIE *leu- "to loosen, divide, cut apart" (see lose). Meaning "not clinging, slack" is mid-15c. Meaning "not bundled" is late 15c. Sense of "unchaste, immoral" is recorded from late 15c. Meaning "at liberty, free from obligation" is 1550s. Sense of "rambling, disconnected" is from 1680s. Figurative sense of loose cannon was in use by 1896, probably from celebrated image in a popular story by Hugo:
You can reason with a bull dog, astonish a bull, fascinate a boa, frighten a tiger, soften a lion; no resource with such a monster as a loose cannon. You cannot kill it, it is dead; and at the same time it lives. It lives with a sinister life which comes from the infinite. It is moved by the ship, which is moved by the sea, which is moved by the wind. This exterminator is a plaything. [Victor Hugo, "Ninety Three"]
Loose end in reference to something unfinished, undecided, unguarded is from 1540s; to be at loose ends is from 1807. Phrase on the loose "free, unrestrained" is from 1749 (upon the loose).
loose (v.)
early 13c, "to set free," from loose (adj.). Meaning "to undo, untie, unfasten" is 14c. Related: Loosed; loosing.