There are two hull forms in the Perry class. Long hull and short hull. USS McInerney (FFG-8) is a long hull version. The Stark (FFG-31) was a short hull. Ships ordered in and after FY79 were long hull. USS McInerney was built as a short hull but was rebuilt as a long hull prototype.
The long hull verions have an extension past the filght deck on the stern.
The thing you see on the stern is a towed sonar array. The Perry will lay the sonar cable out into the water to listen for submarines. The length allows the sonar to listen away from the ships engine and at multiple locations.