If your boyfriend is a US citizen but jobless and you are planning to get married can his mother sponsor you and how does this work?

Your boyfriend can file you, and list his mother as the sponsor. His mother has to earn enough money to be able to support herself and her dependents, as well as you. When she files the paperwork to sponsor you, she is telling the government that she will take care of you. She can be sued if you ever end up getting food stamps or other public benefits.