Bin there, done that. One of the stingers on my GTO was stuck, found the perforated section inside had expanded and wouldn't come through the internal baffles. So, how to pull it out?
The secret weapon was a 1/2'' (12mm) Rawl Bolt (Concrete or masonary anchor). The size relates to the bolt size not the OD of the expanding section. This was then fitted inside the rear of the tailpipe. Used a large washer under the bolt head and a short piece of tube over the exposed section of the bolt, to expand it and lock it into the tailpipe.
Then used a large flat spanner against the washer and a rubber mallet to knock it out. Eventually came out with no damage to the stinger or exhaust. Rounded up the expanded section, good clean and put it back good as new. Brian.
Just add, the perforated stinger section inside the exhaust is lighter gauge metal than the tailpipe. The holes create a weak point which twists and buckles when attempting to free the stinger. This expands the pipe stopping it from coming through the baffles. A design fault really. Fortunately the tailpipe is heavy gauge tube and stands up well to having the rawl bolt locked into it.