To sleep soundly or like a log; a colloquial verb emphasizing deep or heavy sleep.
電車で居眠りして、知らない駅で眠りこけてしまった。
I dozed off on the train and slept so deeply that I missed my stop.
赤ん坊はミルクを飲むとすぐに眠りこけた。
After drinking milk the baby fell into a deep sleep immediately.
会議中に眠りこけるのは失礼だ。
Falling fast asleep during a meeting is rude.