EDIT: Ok, maybe a complete oversight by me here BUT, we are talking 135i and not 128i/125i aren't we? If 128i/125i you can pretty much disregard what I've said above and below as how you've found your exhaust may be how it is supposed to be. If 135i though, keep reading.
Well first things first, what year was your car made? This will determine whether it is N55 single turbo or N54 twin turbo. N54 required four Cats to reduce its emissions, this made the exhaust note quite muted. N55 was more emission friendly and required only one large Cat in the down pipe and as a result is louder than and N54 car.
Can you take a picture of the underside of the axle-back and if possible, what parts of the midpipe you can see?
If they cut the pipe righ by the rear muffler then that's just retarded, there is literally no reason to do that at all when fitting a BMWPE, it's bolt on for axle-back only. My guess is maybe the bolts seized on the flange or it's not a genuine BMWPE; these or the installer was a complete bafoon with no clue.
A genuine BMWPE muffler will have a plate spot welded to it with part number inscribed, can you see if this exists?
The pipe size on the stock exhaust and BMWPE is the same so providing the cuts in the pipe line up, you can fit the stock exhaust just fine. Anyone buying your PE in this case will need to have pipe fabricated and welded onto it in order to fit it to their car, I'd not advise they cut off their muffler