I feel with enough people working together, something could be done. I don't mean to threaten anyone, so let's just say the target is a Fictional Evil Technologically Advanced Billionaire, or FETAB ; and definitely not any real person. The strategy I have in mind would involve digging trenches outside his property and literally smoking him out by burning a huge pile of tires upwing.

The biggest problem would be getting shot by drones while digging or while setting up the pile of tires (if it's done during the purge) or being attacked by police if it's done beforehand. I think secret underground tunnels should start being dug in secret before the purge, so they can collapse into trenches when needed. Then, the trenches keep FETAB from escaping by land in his FETAB-mobile, and the smoke makes a helicopter or private jet difficult to get of ground.

Drones or makeshift aircrafts with makeshift incendiary bombs can be sent to the house under the cover of the smoke. Even assuming he is in an underground bunker, this much smoke would put it's air filtration systems under significant stresses and also cause big material losses. In the end, he still have chances of making it out alive, his death would come either from suffocation in his bunker (if hos filters are saturated by soot and he doesn't have enough bottled oxygen) or, more likely, him trying to escape and having an accident (made more likely by the smoke and trenches).