sleave v.

early 14c., slippen, "to escape, to move softly and quickly," from an unrecorded Old English word or cognate Middle Low German slippen "to glide, slide," from Proto-Germanic *slipan (source also of Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"). This is probably from PIE *sleib-"slip, slide," from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)). The verb is not found in Old English, which did have related adjective slipor "slippery, having a smooth surface." Related: Slipped; slipping. 

It is attested from mid-14c. in the sense of "lose one's footing, slide suddenly and unawares," also "slide out of place," also "fall into error or fault." The meaning "pass unguarded or untaken" is from mid-15c. That of "slide, glide, pass smoothly and easily" is from 1520s.

The transitive sense of "cause to move with a sliding motion" is from 1510s; the meaning "insert surreptitiously, put or place secretly" is from 1680s. The meaning "let loose, release from restraint" (1580s), is probably from the noun sense of "leash for a (hunting) dog that can be easily released" (1570s).

To slip on "put on (clothing, etc.) loosely or in haste" is from 1580s; to slip off "take off noiselessly or hastily" is from 1590s. To slip up "make a mistake, err inadvertently" is from 1855; to slip through the net "evade detection" is by 1829 (for slip through the cracks see crack (n.)). To let (something) slip originally (1520s) was a reference to hounds on a leash; figurative use for "allow to escape through carelessness" is by 1540s.