Rick enjoyed spending Jessica's birthday with her. At the end of the day, he promised to return soon.
Jessica never heard from her grandfather again.
Rick ended up deciding that he couldn't risk ruining Jessica's life. He spent the rest of his life traveling the multiverse, although he never forgot his granddaughter.
Jessica never knew what happened to him, but she refused to let it prevent her from living her life. She continued her work for the service dog shelter, and ended up marrying one of the trainers she worked with. A few years after their marriage, Jessica gave birth to a little boy, who she named Rick.