What’s up with 眠る?

I’ve seen lots of people say it’s a common word that refers to the state of being asleep, while 寝る refers to the action of going to sleep.

But I spoke to my teacher about it today, and she says it’s an uncommon word that usually carries a connotation of death (as in like, sleeping and never waking up).

She’s a native speaker so I’m inclined to believe her, but I’m really confused. Because I’ve tried looking around online and I can’t find anything like what she said.