Are you talking about the icon when you scan a ship, and it says it's travelling? If so, then that goes away when it stops.
I know in certain circumstances you can assign a different pilot and continue on your way. A few weeks ago two of us were in hyperspace in the same ship. about 4/5 through the journey I assigned the other person as pilot, and the journey continued uninterrupted. He got the XP when we arrived.