I grew up with dachshunds, and we currently have one on the strength. He’s snoozing on the bed, with his long nose dangling straight over the edge and his eyes looking at the floor (or would, if they were open). Looks most uncomfortable, but he seems content.
All of the dachshunds we’ve had slept this way, and I don’t recall seeing other dogs do it.
Why do dachshunds sleep this way?
Both of our standard poodles sleep this way. Often they sleep on a doggie bed with their whole body on it except their head which is on the hardwood floor.
My springer spaniel Phyllis does this too, with her head hanging off the edge of the couch, pointing straight down. We tease her about her “broken neck” and say that we don’t want a dead dog – maybe we should get a FRESH dog, a cute little puppy or something. Then she opens her eyes. 
But she also likes pillows and will edge us off ours if we leave any part of them unguarded.
Both springers will lie with their heads hanging off the edge of their foam doggie beds. It’s weird.
Our small and semi-ancient spaniel Bubba does this, as well as fall asleep in various other uncomfortable-looking positions (wedged between his bed and the wall, atop the A/C vent etc.).
[QUOTE=Northern Piper]
I grew up with dachshunds, and we currently have one **on the strength.**UOTE]
umm… what does this mean?
Cats do it as well. Frankly, animals sleep in various positions all the time that I can’t possibly see as being comfortable, but certainly must be or they wouldn’t do it.
[QUOTE=Ethilrist]
“on the strength of the unit” - old military term, meaning currently on the rolls.