Question: What happens to Jennings after Howard destroys the Laser Spectroscope to prevent more Dark Overlords from coming to earth? He is never seen with Howard, Beverly and Phil after it's destroyed.
Answer: He means, what happens to him in that very scene.
Answer: He probably goes back to being a scientist afterwards. Maybe he went into hiding after what he'd been through out of fear of the government wanting to hold him responsible for that power plant's mess.
Answer: As she said to Howard, she believed that he was using his "outlandish" appearance to be unable to find work and collect money through unemployment. She's probably dealt with people who did the same thing and was eventually sick of it.