If a student unfortunately finds themselves in a position of being expelled from their college or university, the stakes could not be any higher. It's all but impossible to get into another school. It's not so much that a student is precluded from applying to another school. It's the fact that those other schools are going to ask about why the student came to leave their former school. In almost all instances, they're not going to be accepted into that next school. That's the unfortunate reality.
A student does have rights though. They would have often the right to appeal the expulsion through the school process. The particular college or university's school policies would have to be referenced regarding what the appeal rights are. Often there's a short deadline to submit an appeal. If a student is sanctioned, whatever that sanction may be, including expulsion, depending on how the case got to that point, if there were any failings on the school part, a student may have other rights, say rights under due process. If it's a public university or contractual rights, if it's a public or private university, where if the school failed to follow its procedures or if there were missteps in the process that led to that expulsion, those kinds of arguments can be raised often best at the school level, often say if an experienced attorney is involved, he would do so with the school's offices, general counsel as needed. It doesn't actually have to go to that step immediately, but on an as needed basis. It needs to be rectified because if that expulsion stands, it's going to put that young person in a terrible position moving forward.
An experienced attorney needs to be involved, especially at that stage, but to avoid that from happening as early as possible and the process is going to maximize the prospects of success is going to minimize the likelihood of some kind of severe sanction such as that.