If a woman owns her home and she and her boyfriend have lived together 28 years and she dies, does he have any rights to the home?

He is not entitled to any share of the home.  However, if she leaves it to him by will then he would get it.  Under the laws of intestate succession if there is no will he gets nothing.

I am sorry for the loss here and for the situation as iot appears to be.  Does she own the home?  Meaning is she on the title to the home?  Or did he leave it to her in a Will?  If the answer is no then she will not inherit via the intestacy statutes in the state, which govern the distribution of an estate in the absence of a WIll.  Please seek legal help here.  Good luck.