I haven't experimented with bullet in that way yet. A -possible- solution with the cloth sim is to place a primitive partially in the dresser top. Place the d-cloth -over- the primitive, with collision set on the primitive and the dresser top. Once you have that, move the figure hand =over and around= the primitive, as if clutching it, then parent the primitive and -only- the primitive to the figure hand. Your crashing is almost certainly caused by collision errors a dense mesh with cuts in it can cause. By 'trapping' the cloth between the primitive and the hand, you can adjust the distance between them, giving the cloth room to bunch and gather around the low res primitive, and just using the the primitive to do the actual cloth moving, while the hand just covers up the trick you are using.

The only other option with a 'held rag' would be to model the part the hand holds as a solid mesh, then attach the dynamic part to that. The whole goal with dynamics is to keep the cloth from being pinched between two pieces of geometry; that will stall or crash the sim instantly.