There are some historical examples, but few. Most often, when a scabbard was worn on the back (or perhaps more accurately, the shoulder), the scabbard was removed from the back/shoulder before the sword was drawn. The scabbard was slung over the shoulder for convenience in carry (like a shoulder-slung rifle). Some examples:

• Odachi: https://en.wikipedia.org/wiki/File:Samurai_wearing_a_nodachi_(field_sword).png

• Odachi: https://en.wikipedia.org/wiki/File:Hiyoshimaru_meets_Koroku_on_Yahagibashi,_showing_nodachi_or_odachi.jpg

• Dadao: https://i.pinimg.com/originals/b8/cf/fb/b8cffb96e2e83cb3f92781f751dddb1e.jpg

Odachi were very large swords, and this carry kept them away from swords worn at the waist. Large swords like this were often (sometimes in scabbards, and sometimes bare-bladed) just carried on the shoulder; slung over the shoulder leaves the hands free, but it makes it slower to get the weapon into use. For Chinese dadao, this carry is very late, when artillery, machine guns, and rifles dominated the battlefield - the rifle would be the weapon of first choice, and the sword is carried to keep out of the way of using the rifle. It's like a backpack - when you want to take something out of one, you usually take it off your back. Wearing it on your back keeps it out of the way, and both hands free,

There are also some examples of back scabbard, with the sword hung from a belt with a scabbard slide. This appears to be to enable charioteers to wear a sword on their belt without it getting in the way.

• Qin Dynasty Chinese example: https://i.imgur.com/vDN0RYC.png

• A Celtic example, but we can't tell if it's a charioteer: https://i.imgur.com/0zj5FJX.png - from the Withemsea (North Humberside) chalk figures

Qing Dynasty soldiers often wore their sword scabbards tip forward, hilt back:

• https://upload.wikimedia.org/wikipedia/commons/8/8d/ChineseSoldierByWilliamAlexander1793.JPG

• and a Korean example: https://i.pinimg.com/564x/e9/d4/d0/e9d4d06b95bf46fea91689270947b6f6.jpg

People have experimented with this, and it is possible to draw the sword from the back, reaching around the back with the right had to grab the hilt, and then drawing the sword. A similar draw would work with this charioteer sword. (Whether such a draw was usually used by these Qing soldiers, we don't know. The scabbard can be turned around and the sword drawn in the conventional manner.)

Finally, the SE Asia dha (or daab) is sometimes said to be worn on the back, but the usual carry is hung under the arm: https://commons.wikimedia.org/wiki/File:Kachin_tribe_depiction,_1900s.jpg

And if they were what advantages or disadvantages did they have?

If the sword is large, it can't be easily drawn from the back. If the sword is small, it can be drawn from the back, but this necessitates more movement, takes longer, and exposes the swordsman more than drawing from the waist.

There isn't much benefit, but it can be easier to carry very big swords on the back (or shoulder), and the charioteer examples suggests that keeping the hilt away from reins can be useful.

Wearing a sword on the back does keep it away from the legs, but this can also be achieved by wearing it through a waist belt, or hanging it fairly high from a baldric or a waist belt. Low-slung swords can get in the way of the legs, but that's typically a cavalryman's carry for a sword, and was often lifted higher when they dismounted.