cleft n.

"to split, part or divide by force," Old English cleofan, cleven, cliven "to split, separate" (class II strong verb, past tense cleaf, past participle clofen), from Proto-Germanic *kleuban (source also of Old Saxon klioban, Old Norse kljufa, Danish klöve, Dutch kloven, Old High German klioban, German klieben "to cleave, split"), from PIE root *gleubh- "to tear apart, cleave."

Past tense form clave is recorded in Northern writers from 14c. and was used with both verbs (see cleave (v.2)), apparently by analogy with other Middle English strong verbs. Clave was common to c. 1600 and still alive at the time of the KJV; weak past tense cleaved for this verb also emerged in 14c.; cleft is still later. The past participle cloven survives, though mostly in compounds.

Proto-Indo-European root meaning "to tear apart, cleave." 

It forms all or part of: cleave (v.1) "to split, part or divide by force;" cleft; clever; clevis; clove (n.2)  "slice of garlic;" glyptodon; hieroglyphic; petroglyph.

It is the hypothetical source of/evidence for its existence is provided by: Greek glyphe "a carving," glyphein "to hollow out, cut out with a knife, engrave, carve;" Latin glubere "to peel, shell, strip;" Old High German klioban, Old English cleofan, Old Norse kljufa "to cleave," Old Norse klofi, Middle Dutch clove "a cleft."  

Old English clif "steep and rugged face of a rocky mass, promontory, steep slope," from Proto-Germanic *kliban (source also of Old Saxon clif, Old Norse klif, Middle Dutch klippe, Dutch klip, Old High German klep, German Klippe "cliff, promontory, steep rock").

Clift has been a variant spelling since 15c. and was common in early Modern English. It represents an influence by or merger with clift, a variant of cleft (n.). Cliff-dweller first attested 1879, American English, in reference to aboriginal tribes of the U.S. Southwest who built dwellings in natural recesses in cliffs.