Can my ex-wife's boyfriend claim my son?

My ex-wife and I have shared custody, but he lives with me year-round (she sees him every other weekend).  We are supposed to alternate tax years, but I suspect she had her boyfriend claim him to avoid having her taxes garnished for unpaid child support. She doesn't work, but says she made enough through plasma donations to file taxes. Can he claim my son if they're not married?  Can she claim him at all if she has no income (I suspect he claimed her as well, plasma donations notwithstanding). If it's not allowed, what can I do?