That depends though, If I'm only hopping between airports within the Charlie airspace, than TRACON will issue a local code, (02**) no handoffs because I'm not leaving their airspace. What I was referring to in the post you quoted, was for a flight that terminates outside of the TRACONs airspace who issued the original code. In that case they put you 'into the system' (unsure of proper terminology) and issue a code that is passed along through each sector.
With FF being a service provided "when able", they really don't *have* to put you into the system and sometimes don't.
They may decide they have time to handle you to the edge of their airspace and will accept you, and put you on a local code, but are fully planning to dump you at the edge because they don't have time to put you in, or coordinate the handoff, or they know the Center isn't being cooperative today, or whatever.
Or maybe they intended to put you in and issue you a new code and then five other aircraft called up so it isn't going to get done before you hit the edge.
It's fine, really. You can't really tell why.
You just get "radar service terminated" and start over. Call up the next folks and see what they can do. No big deal. It's FF.
The nearly guaranteed way not to have to change a squawk very often, is to earn the Instrument rating and file.
Then you're truly in the system and they're probably going to know you're coming.
FF, there's no guarantees.