I dug up the FDOT Shapefiles (as of July 30 of this year) and it appears that the Road ID for SR 404 (70004000) terminates at Wickham Rd (CR 509), and the extension (which has a different ID, 70000402) continues on a different ROW past Wickham to I-95. The shapefiles also include the interchange with I-95 complete with ramps.
So just because the Road IDs are different doesn't mean SR 404 (the designation) won't be extended westward to I-95. It could also be the county road designation that gets applied, but I highly doubt that if *SR* 404 is already signed on the BGS's on I-95.
NE2, the road I mentioned above (70000402) exists from CR 509 (and beyond to I-95) to just west of the interchange with US 1. Is this signed as CR 404? The road above which terminates at CR 509 (and doesn't go any further, except to a residential area) is the original 70004000.