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I don't think a general solution exists, this is just the unfortunate choice that was made by the graphics industry to use linear algebra matrices to represent scene graph kinematics...
They should have picked dual quaternions, or more generally Clifford algebra instead, and keep scaling as a final deformation stage, but they didn't. So now we're stuck with these singularties forever ;)
See e.g. the test scene
ZeroParentScaleTestAnim.ma
Related to #136
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