Image textures have a "Clip Cube" extension mode that sets all areas outside a cube around the image as transparent.

Is there a way to set to a default value instead of transparency, somewhat similarly to how the "Extend" mode extrapolates the nearest pixel value? It should work with modifiers.

This is both a subset of and a workaround for the behaviour that used to be possible with voxel image sequences, so if there is a way to get those back then that would also count as a solution to this problem.