I guess the issue is that the shape keys do not exist on the mesh anymore after modifiers are applied. So the data path does not exist on the parent, when the driver is evaluated.
I don't really see how that could be fixed in a good way...

@Sergey Sharybin (sergey) Any ideas? Should this work currently?

(Copy-pasting my comment from T74207):

The issue here is that the drivers gets evaluated by the depsgraph, using evaluated datablocks. And evaluated objects have evaluated obdata (like mesh) from modifier stack, which obviously have no shapekeys anymore (since those shapekey data would be completely invalid for the mesh generated by the modifiers most of the time).

Am not sure how to fix that best tbh, @Sergey Sharybin (sergey) Sharybin (sergey) might have ideas here?

@Bastien Montagne (mont29) To me that sounds like this is not a bug in Blender but a known limitation. There is quite a simple workaround: add a few custom properties and use those to drive the shapekeys on both objects. Here is a demo:

@Sybren A. Stüvel (sybren) wouldn't mind having some depsgraph expertise on this topic first. If (as I suspect) this is not easily solvable, then yes, think we can consider it a known limitation. But if some relatively simple solution exists, then I think the issue is important enough to be considered a bug. :)

@Sybren A. Stüvel (sybren), this used to work before dependency graph changes done in 2.80, so is something to be fixed in one way or another than to be called a limitation. "New" dependency graph is to allow having more comprehensive setups, not to introduce limitations.

@Bastien Montagne (mont29), simple idea: allow evaluated mesh to reference shapekeys with mesh it was crated for, Will keep RNA paths valid, and should not cause issues: sine evaluated mesh is not meant to be re-evaluated, so shapekeys will be ignored.