The school has an administrative appeal procedure available to students at risk for discipline such as suspension or expulsion. However, the administrative appeal system typically must be invoked and pursued by the affected student within a very short time-period. If the student pursued an administrative appeal and was still expelled, there may be rights to judicial review of the factual basis for the school's determination. But that recourse, too, must typically be pursued in a very short time-limit.
It does sound as if your friend may have let some significant time elapse following the school's action, but your post is unclear on that critical point.
If the student did not invoke the administrative appeal process offered by the school, then it is highly likely that there is any right to bring a legal action in court. Schools have a lot of latitude for running their business and the courts will not ordinarily interfere on behalf of those who did not first use the available administrative process.
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