Yes it is repairable. Pull the radio and then you can pull the face plate of the radio off then you can see the AUX plug and it's solder connections.
It isn't uncommon for one of the AUX plug pins that is soldered to the board to break off the board, and re-soldering the pin to the board is easy repair. If for some reason the AUX plug is broken in some other fashion the plug can be replaced.
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08 FLTR candy red sunglo,with 2015 103 HO, V&H Dresser Duals with Monster Rounds, Power Vision tuner, Willy Shiny Wheels and Forks and a bunch of other stuff.