why would you want to go after them. I would be happy they left. The only time I would pursue them is if there was a abduction. (unless it was my first wife, then I would take a few days to report it )
After a home invasion, IF the BG leaves, your only duty is to be a good witness for the police.
There was an old saying, If your shoot them and they fall outside your house, drag them back inside, then you won't be charged. That pretty much applies everywhere except NJ and Mass. Those two states have the "UK" attitude