How to support a partially demolished chimney
I would remove the remaining chimney. Having a massive chunk of heavy brick and mortar suspended from the upper part of the structure is not something I would want hanging over my head. 

If you live in an area where there is any chance of an earthquake would put more than triple concerns and impetus to get it removed.

You do have real concern that the thing could come crashing down if you start trying to remove it so you would really need to devise some decent support under the thing to prevent it from crashing. Such support can be temporary. After proper support removal should be done from the top down a brick or two at a time. 

I removed part of an old chimney this way and found it was easy to dismantle because the thing was originally made with sand/lime/horse hair for the mortar. It was a simple process of just unstacking the bricks.