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p. 141 of the DMG, "Paired Items":

Items that come in pairs-such as boots, bracers, gauntlets, and gloves-impart their benefits only if both items of the pair are worn. For example, a character wearing a boot of striding and springing on one foot and a boot of elven kind on the other foot gains no benefit from either item.

For the question of whether you fall off the ceiling if you fall unconscious, I would first like to remind that these are magical slippers. They work because of magic. They don't care about the physics of the surrounding environment, because they work through being powered by magic. Secondly, it says you don't need hands to walk along vertical surfaces. Depending on how a person imagines this is interpreted, one could think of someone stepping into a vertical surface only with the balls of their feet and bending their foot so they face upright as they walk up. One could also imagine a person being completely perpendicular to the vertical surface as they walk along it. Both would be correct given the description of how the item works. Let's assume a person is perpendicular to the vertical surface. In that case one could also argue that the character must use their core strength and leg strength to hold that perpendicular position, because, if it's just the "stickiness" of the slippers holding the character to the wall, then there's a lot more to the physics of holding someone in that position. Also, there's the whole concept of these being slippers, so they either stay on magically, or, because of gravity, the character can just slip out the backside of them. I describe all of this to say that there's obviously a whole lot more going on here to keep a character on that wall than just sticky shoes. Likewise, if a character was upside down, they might slip out of the shoes as well, and also be subject to all the blood rushing to their head after a prolonged period spent upside down. In my opinion, none of those explanations via physics are very fun. Magic ignores physics and gives the effect that it describes, because the magic user who created the item, spell, magical effect, etc. stated the exact effects that would take place when they wove the magic. So, all of this being said, how would I rule as a DM if someone was knocked prone as they were on the wall or ceiling? I would say that they go prone right where they are, be it a wall, ceiling, or other surface. I can hear the weeping and wailing of the nerds already. "But gravity, but physics, but the rest of the world around them!" That will be the beginning of said complaints as they gnash their teeth and rip their clothes. My reasoning? It's magic. 

In reality you are correct but DND is just for fun. As a DM I'd allow it. Have fun adventuring everyone!

Under rules as written, search the Player's Handbook for the definition of attunement, it does not require you to be conscious to maintain attunement with an item.

If you are dead on the ceiling however, you fall from the ceiling, as that is one of the ways to break  attunement.  If you merely sleep on the ceiling, you sleep like a bat hanging from the ceiling. 

Depends on your dm. I had my player hang their untill brought down with a ladder.. 

If I have a carpet of flying and these slippers can I ride the carpet upside down 

i think if you had 1 leg you would have half a walk speed or something, so the smae would apply to the slippers, and you would have halved climb speed (15 if you have 30, 20 if you had 40, 17.5 if you had 35, etc). this is just my interpretation and you should ask your dm

I say the shoes stick but you fall

You could stick but only on the foot

Yes! Thank you! I'm only in the comments section to see if anyone else thought so

Quote from MajordomoTom >>

Under rules as written, search the Player's Handbook for the definition of attunement, it does not require you to be conscious to maintain attunement with an item.

If you are dead on the ceiling however, you fall from the ceiling, as that is one of the ways to break  attunement.  If you merely sleep on the ceiling, you sleep like a bat hanging from the ceiling. 

 I think this is the best answer. I'm gonna stick with this. Thanks MajordomoTom!

i think if you had a fake leg or something like that it might work although it is up to the dm