Would you leave your man?

Okay me and my boyfriend are 18. We've been together a year, and he has really strict parents. We both just graduated high school, and neither of us have jobs. But his parents decided to kick him out over a huge argument they had. My parents are strict and won't let him stay with us. Well he told me the only place he has to go is is ex girlfriends. His ex is a horrible person. From day one she's been trying to break us up. Starting lies that he's cheating on me, always inviting him to over so they can get back together, sending him nude pics. Well anyways he told me that's the only place he has to go, so he has to stay with her for awhile. This really worries me. He says he has no other family or friends, she's literally the only one. I just don't think I can handle him sleeping at the same house with the girl who will do anything to get him back. We've had a great relationship, no trust issues even with this pysco girl in the picture but idk.  Would you leave or should I just stick it out?
🔸he slept in my car last night, he doesn't have friends. Most of our friends are 17 living at home with their parents