Can we fight this recent employment issue?

My boyfriend had a job but was searching for something with more stable hours and higher pay. He found what seemed like a great job opportunity and was offered the job right in the interview. They told him after the background check and references were taken care of, he would be sent the new hire information via email. He received the paperwork a couple days later and started the job this past Monday. He quit his other job to take this job. It’s now Tuesday and he was just fired! The employer told him they called one of his past jobs and found out he wasn’t rehireable for that company (he quit the job without notice, nothing too terrible). Due to the fact that this current company works for his past job, they can’t offer him the job anymore. He was never told this. He was never asked if he was rehireable with that past job. So, he left a job to take this one, and now he has zero jobs. We have no idea what to do or if that was even legal. Why would a company call previous employers after they have hired an employee and they have started working there? Doesn’t that seem completely backwards? Obviously, if he had been told that the decision to hire him would be based on whether he was rehireable at a job he was at over 2 years ago, he wouldn’t have taken the job. Any advice? Family members have told us to get a lawyer but I’m not sure its legal and don’t have any money to spare on a lawyer if its not worth it.