What did you do with the money that was left.?
Is there any milk [that is] left?
So do you think these sentences are unnatural with relatives ?
The first is fine.
The second is fine - without the 'that is'. It is unnatural with 'that is'.
My personal feelings are backed up by the number of citations in COCA. There are 31 for ' is/are there any [noun] left' and none for 'is/are there any [noun] that is/are left'.
Then what about this: I don't know anything about the box that is locked (is it natural?)
That's fine, but irrelevant. "I don't know anything about the box locked" is not natural.
'Left' is, as Swan says, a special case.
Student or Learner