Ask to the seller send photos of GPU-Z, check de informations in techpowerup like GPU code, Cores, TMUS, ROPS, Memory Type, BUS Width, it never fails.
It will prove if the gpu is working and if it's a 1080Ti
I think the only way to verify the integrity of the card is to choose a technical assistance in the seller's city, and ask him to take the card to the chosen location before purchasing it.
They are often boards used for cryptocurrencies that have a very low lifespan, anyway, I don't recommend them.
Low frame rate or stuttering during gameplay is a major sign of graphics card deterioration. Poor frame rate in the game or a screen freeze indicates a problem with the graphics card. But in-game crashes can also be caused by malware or RAM if there is no sign of this, your video card is good