Continental Calving

You know how glaciers calve into the sea, creating icebergs, right?

Antarctic Glaciers 

After the Tsunami of 2011, I began to wonder if the same thing could happen the subducting earth's crust going under a continental plate.

Geology Cafe 
 Wondering what might happen if it just snapped off and sank into the asthenosphere? It probably just melts at the end and is absorbed, but what if it snapped? Would a giant fissure open up, flooding lava to the surface?