I like doing what we call BP +1. Put the IF and OF defense in their spots. Take a normal round of BP but on the last pitch it's live. But no matter what they hit they have to stretch it to an extra base. For example a nice easy single over the SS head to the LF - the batter has to stretch it into a double. Now the defense has to play aggressively and the runner can start learning what they can / cannot stretch into extra bases. Once you get the hang of it then on a play like this have the runner put the brakes on and now the defense has to execute a rundown.
If the ball hit is a simple grounder and he gets thrown out at first now you can work on a bad throw situation. Once the first baseman catches the ball he steps forward, turns and throws the ball somewhere in foul territory. Now the catcher is involved and the runner breaks down past the bag like normal and then breaks to second.
On the baserunning out / safe doesn't matter. Once the play is over then the runner goes to the nearest base and works on reading bunts, hit/run, sac flies - whatever you're doing in the normal part of BP before the last pitch.
You can get a lot of realistic situations in that way while teaching aggressive baserunning.
Also, going back to the double relay thread since you're doing BP pitching there's probably going to be several balls in the gap / fence. Great way to work on this and even with a runner on first to work on that plays at home.