Back in the G4 days, you can get bumper cases that literally is only a bumper around the edges. Protects edges/corners, keeps screen off table, doesn't hold heat in the back.
Nowadays, searching for bumper cases they all have a clear back. Is that it? No more edge only protection? I prefer to go caseless, I want my phone to stay thin.
For LG G7 in this instance.
OP already says they searched for the case. Your search suggestion doesn't answer yes or no, but it shows similar cases.
I had this problem today with the S8 I just bought. I think it stems from the fact that phones these days have a glass back and so the manufacturers want to protect it as well.
the S8 has a case that doesn't cover the whole thing. it's called the 2Piece Cover.
Jetech do bumper and back panel plastic cases which can be easily removed.
Example: https://www.amazon.com.au/JETech-iPhone-Shock-Absorption-Bum…
Maybe you can do the same for this: https://www.amazon.com.au/ProCase-Hybrid-Crystal-Protective-…
I saw another picture of this type, and it looked like the back part provides some thickness that the edge needs to cling onto, or maybe the back silicon provides grip. Not sure if it works without.
Some of them you can see without the back piece the side bits will flap around with the lost thickness. The Rinke one especially with the thick back
But I'll ask the seller see what they say.
http://bfy.tw/Mg3d