Technically, these are called InCopy stories, not assignments (assignments are like mini-layouts you can create in the Assignments panel, that hold collections of InCopy stories).
Anyway …
If you place the same InCopy story in multiple documents, and this InCopy story had a cross-ref, what do you *want* to happen to the cross-refs in the duplicate stories? (I’m not following you, I guess.)
InCopy story A has a cross-ref to chapter 2 in InDesign file A.
You place the same InCopy story in InDesign file B.
The cross-ref will report that it’s missing the destination in file B, even if file B has a chapter 2.
That’s because cross-refs are hard-wired to the name of the InDesign file they’re pointing to. The story in InDesign file B knows that it’s “lost its mama” and so reports her as missing.
If you update that story in layout B (you’d need to check it out) and point the x-ref to chapter 2 in layout B, and Save, then the story in layout A will report as being out of date, because you edited it. When you place the same InCopy story in multiple files, it’s like placing the same PSD or TIFF in multiple files. Edit one instance, all instances need updating.
So the answer is: You can’t do that, sorry. You can continue using InCopy stories (or use Edit > Place and Link in CS6 and CC), but you can’t use x-refs in them.
AM
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