As Nippymog says, that looks like the catalytic converter has disintegrated. If you look up the tail of the exhaust header pipe you should be able to see the end of it, it looks like some rolled up crinkly cardboard packaging. If the one side has gone I would be tempted to remove the cats entirely from both sides, others have done this without issues. There is no material like this inside the standard Morgan exhaust, only very restrictive baffles. The quieter and free flowing G56 system does have material inside them as they are absorption exhausts.
