c. 1300, sauf, "unscathed, unhurt, uninjured; free from danger or molestation, in safety, secure; saved spiritually, redeemed, not damned;" from Old French sauf "protected, watched-over; assured of salvation," from Latin salvus "uninjured, in good health, safe," which is related to salus "good health," saluber "healthful" (all from PIE *solwos from root *sol- "whole, well-kept"). For the phonological development of safe from sauf, OED compares gage from Old North French gauge.

From late 14c. as "rescued, delivered; protected; left alive, unkilled." The meaning "not exposed to danger" (of places, later of valuables) is attested from late 14c.; in reference to actions, etc., the meaning "free from risk," is recorded by 1580s. The sense of "sure, reliable, not a danger" is from c. 1600. The sense of "conservative, cautious" is from 1823. It has been paired alliteratively with sound (adj.) from c. 1300. In Middle English it also meant "in good health," also "delivered from sin or damnation." Related: Safeness.

prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not."

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

Often euphemistic (untruth for "a lie") or emphatic, if there is a sense already of divestment or releasing: unpeel " to peel;" unpick "pick (a lock) with burglars' tools;" unloose for "to loosen."

It also makes words from phrases, such as uncalled-for, c. 1600; undreamed-of, 1630s. Fuller (1661) has unbooklearned. A mid-15c. description of a legal will has unawaydoable; Ben Jonson has un-in-one-breath-utterable. The word uncome-at-able is attested by 1690s in Congreve, frowned at by Samuel Johnson in the 18th century and by Fowler in the 20th ("The word had doubtless, two or three centuries ago, a jolly daredevil hang-the-grammarians air about it ; that has long evaporated ; it serves no purpose that inaccessible does not ....").

But the practice continued; unlawlearned (Bentham, 1810), unlayholdable (1860); unputdownable, of a book, is by 1947; unpindownable, by 1966. Also compare put-up-able-with (1812). As a prefix in telegraphese, to replace not and save the cost of a word, it is attested by 1936.

With the variety of its possible use, and the need for negatives, the number of un- words that might be made in English is almost endless, and that some are used and some never is owing to the caprice of authors.

Dictionary editors noted this since 18c. but also padded the list. John Ash's "New and Complete Dictionary of the English Language" (1775) has many pages of one-line un- entries; among a dozen consecutive entries are unhaggled, unhaired, unhalooed, unhaltering (adj.), unhaltering (n.), which sorts of words OED (1989) notes were "obviously manufactured for the purpose" and some turn up in other texts only decades later, if at all.