Originally Posted by Ford_6L_E350
The rod welded on the tailpipe is the standard Ford hanger. I don't know what the other round thing that may be attached to the tailpipe is - never seen one like it.
Its a Vibration Dampener. Its weighted to absorb any vibration caused in the pipe. Car companies put them on exhaust systems, drive shafts, axles and transmission mounts sometime to eliminate and harmonic imperfections or imbalances.
After looking at mine I see tail pipe hanger is attached to the bottom of the frame rail not inside like yours. I did see another post on here that was more like yours though. Mine is a 2008 V-10 so in might be different as they most likely change from time to time and would be different depending on pipe size, motor type and size, parts/supply availability and such.
If you are having vibration issues you might check to see if the tail pipe hanger/rod is just touching the inside of the frame as it looks close in your second picture. It might show as a rust or bare paint mark wearing on the frame where the hanger rod sticks though the rubber part.