That glasspack-like device is a resonator. It removes drone and rasp from your exhaust note. On a completely stock system you can remove it and get some more sound. However, once you delve into headers and such, you'll be wanting one back (aftermarket exhaust or no).
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'13 Mustang 3.7V6 - MT82
'00 GP SE (L67 Swap, XP, Headers, 3.25")
'98 GTP, '01 Bonne