Yes, here is why some material moves inwards... (Score 1)

As I said above, in my research I have found inward moving ejecta. This has been seen by other researchers too.

I have explained it as being due to interaction with the external medium. If you have a much lower density on one side of the supernova remant than the other it will set up a pressure gradient within the remnant which pushes material to the less dense side. This has been confirmed through numerical hydrodynamic simulations.