9mm. Bore brush is a no-go. Don't want to wait several days for cerrosafe.

Try a .40 or .45 caliber brush.

Doesn't budge.

Possibly a 9mm tap or 3/8 tap to try and bite into interior case wall and pull it out ?

Maybe heat chamber end and see if remnant come loose,, but I am not up to speed with expansion rate of brass vs steel

Have any canned air? use the red tube and spray the crap out of the remaining case, you want it COLD. The brass will cool faster than steel and will shrink away from the chamber walls. Immediately, insert the over size bore brush from the chamber end if at all possible and go completely thru the case, this will give the bristles the best bit when you pull it back out...

Once you go past pen oil and chamber brush or freezing, cerrosafe is next inline for safe methods. You can, try an easy out of the correct size, or, tap that just threads into the case. With either, you will want to tap them out from the muzzle end with a brass or wood dowel. I have read of folks using epoxy in place of cerrosafe, also, low temp solder could be used. Heck, you could even use lead for that matter, just be careful of any contaminants, that could react with the much hotter,molten lead...

If it is a split ring, get a 3/8" dia x 5 or 6" long bolt with course thread.

Get a socket and extension tool to drive it into the brass ring clockwise until it's snug.

Now insert a brass rod from the muzzle end into the barrel.

Lightly tap the end of the brass rod with a small hammer as it makes contact on the bolt you just inserted.

This should extract the brass ring with NO damage to chamber if you take your time.

Do not use a tap, a drill bit, or anything that is hardened.

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I've used a tap several times.  Use one small enough that doesn't bang into the chamber but will barely bite into the case.

I have a broken shell extractor for 5.56/.223.  Do they make something like that for pistol/rimfire cartridges?