As-is, Aurora has the weird situation where an unexplored JP is "safe" in that nothing can unexpectedly transit. Active NPR's, if you have them, can potentially find a JP leading into your systems or into explored systems that you border, but those create new JP's not unexplored ones(EDIT: This isn't true, they'll link to an unex if one exists- thanks Bremen).
The idea to change that would be that when a NPR or player race enters a system, the game immediately generates all the JP's and the systems that those JP's connect to. So at the start of the game all the systems adjacent to Sol have already generated, and when one of them is entered by the player(or if it generates an NPR in one, immediately) all the systems adjacent to that system are generated.
Potentially this could be configurable as a depth to generate, where 0 is the current behavior, 1 is the above, and 2+ would mean it would generate all the systems within however many jumps of the entered system.
Overall I think this would make it less favorable to turtle in Sol, give NPRs some more time between their activation and when the player(or other NPR) can actually engage them, and limit the gamey-ness of JP exploration a little. At a guess the cost would be to the number of systems generated at any time(I think this is minor), and also to the number of active NPRs which probably isn't.