Can a 14 year old live with 22 year old man?

If you mean in a relationship, not she can not. Sex with the minor would be statutory rape and a minor cannot move without parental consent. if they by chance would allow the minor to move the CPS would put the 14yo in foster care and the parents lose their parental rights.

If you mean like a legal guardian, in a parents place, yes you can if the 22yo is found fit by the court.