An issue recently came up about the inheritance rights of illegal immigrants in a Market Watch article "My brother-in-law is an undocumented immigrant -- can he inherit my sister's house?"
A woman wrote in explaining that her deceased sister had been married to an illegal immigrant for 30 years. The husband, who had never applied for a green card or U.S. citizenship, was afraid to put the house in his name and claim the inheritance, because he fears deportation.
She wondered whether he can inherit the property.
The simple answer is that he can inherit the property.
With some restrictions foreigners can own real estate in the U.S. Estate law does not discriminate against non-U.S. citizens.
Of course, that does not mean that the husband cannot be deported.
Reference: Market Watch (November 27, 2016) "My brother-in-law is an undocumented immigrant -- can he inherit my sister's house?"