Only idea without removing transmission is possibly use a strong vacuum cleaner as you break it into little pieces, but I bet there is limited room to get something like that in there.

Otherwise you probably should change filter and fluid shortly after you do this work, as the little piece should be filtered by the filter.

Good luck

dlm4ut

 

Actually any pieces that fall, will fall between the flywheel and the torque converter. They won't get into the engine, because of a rear seal and they won't get into the transmission because of the front seal. Any pieces not retrieved however will be thrown around if not removed.
I had this same problem on a Chrysler Imperial. The best thing to do is not break it below the transmission surface. Hopefully you have some of it extruding out. WD-40 is about the best suggestion.
Drilling it out through the center is not possible with a regular drill bit. It has a magnet in the center which is harder then the average drill bit. I was going to drill through it and put an easy out in to pull on. A diamond tipped drill bit may work though.

I ended up pulling the engine out for other reasons and used a rubber mallet to hammer it out. Which was still a pain in the butt to accomplish since it was so corroded in.
Good Luck.

 

If you are going to try drilling and easy outing, or if your going to try breaking it out, remember the following.
It's pointed at the flywheel and has a small gap between. Be careful when hammering or drilling through it. If it starts pushing down it will hit the flywheel, possibly causing the flywheel to be bent. Which means the tranny or engine will need to come out. If you choose to drill it, to remove the magnet, so it's now just a piece of plastic, or try an easy out through the magnet,don't drill all the way through, or be careful if you do.
The sensor looks for holes in a flywheel. When it sees one,it fires the corresponding plug. If you drill a hole through it, it'll mess up causing unknown problems. Depends on where the hole was put on the flywheel. To be safer, roll it up on top dead center of cylinder 1. Then drill. Better chances the flywheel has cylinder ones hole right where your drill bit could go through as your drilling through. It may also fit through that hole and drive down. You would need to remove the four torque converter bolts and push the torque converter back or maybe roll the engine around by hand to remove it. This would be my last resort personally. I'm not positive it will fit through the hole or actually fall out when you did punch it through.
Definately use a vacuum source with either choice. Keep those pieces from falling down. Mostly because the easiest way to get to them is through the starter hole, once it's removed. The flywheel cover won't do. There isn't enough room between the flywheel teeth and the tranny housing to get bigger pieces through. They will fall right behind there though.
Using a smaller flexible hose and duct tape make yourself a siphoning tube that is functionable in the area you are working. Adapting from a crevice tool on a vacuum cleaner is suggested. It'll also help later if pieces do fall down. You'll be able to reach through and down where the starter was removed from. Or through the flywheel cover to finalize getting the dust.
As long as you don't crack the tranny housing from hammering (use of rubber mallet causes this to not happen), mare the transmission housing in the hole with a drill bit or whatever, lose pieces of the magnet and you do not damage the flywheel, you'll be ok, that is the only damage that can be done.
Clean the hole out with some emery cloth when you do get it out. Don't force your new one in or it'll have the same problem down the road if it ever needs replaced again.