A party your non friend makes you go to by laying on a guilt trip or by pulling out a gun. You know this party is going to be awful and cost you a lot of money, but you go anyway because it's better than spending the night watching reruns of Hoarders.
A punishment party usually happens as punishment for having too much fun, but can happen for other reasons as well.
"This is like the worst party ever. It's like a punishment party. I only got a salad and they made me split a $200 bill. Half the people are creepy and the birthday girl keeps making out with some ugly dude"