Attached is a simple scene with a skydome and a background dome inside of the skydome with render stats "Casts Shadows", "Receive Shadows", "Double Sided", "Visible in Reflections" and "Visible in Refractions" are all set to off.
Using RTX 2080 TI or CPU rendering the scene renders fine, however, when using a GTX 1080 is seems as though this background dome blocks the light from the skydome and actually casts shadows and anything inside of it is dark.
Also Arnold > Visibility stats "Primary Visibility", "Casts Shadows", "Diffuse Reflection" and "Specular Reflection" are set to off. When the background dome is hidden the object inside of the dome is visible when rendering with the GTX 1080.
yes I did the background dome casts its shadow and it's odd that you managed to render it with 2080 TI I'm using 1080 TI as far as I know matte and visibility isn't supported now you can assign the background dome texture to camera visibility of the dome light as a workaround, please check again and make sure you can render it with 2080