'Sleep' may relate to 'going slack' — the body going limp as consciousness departs.
To rest with the eyes closed in a regularly recurring state of reduced consciousness and bodily activity.
From Old English 'slǣpan,' from Proto-Germanic *slēpaną, possibly from PIE root *sleb- or *slāb- meaning 'to be weak, to sleep.' The word is confined to the Germanic languages and has no certain cognates outside that family. Some scholars connect it to Lithuanian 'slòbti' (to become weak) and Old Church Slavonic 'slabŭ' (weak), suggesting the original sense was 'to become slack or limp' — a metaphor of the body's collapse into unconsciousness. Key