The short answer is yes, if for example what’s posted can be seen as defamatory, illegal or false. The action that can be taken against somebody will depend on what was posted and what action the ‘offended person’ wishes to take.
This may include making a complaint to the police or the University. The University has a policy to stop behaviour that might ‘bring the University into disrepute’. Their harassment and bullying policy also applies to behaviour online.
Sometimes posts can be made in haste, anger or frustration, so before you reply to something or share how you are feeling, just check how it may come across to people reading it. It may not be meant as malicious or defamatory but if the person receiving it, or others who see it take it as such, then they can take action. Once you post something you are no longer totally in control of it; evidence isn’t easily deleted and could be circulated to someone you didn’t want to see it.
If you’re studying law, teaching, social work or healthcare your individual professions will have guidelines about how you should behave online as a student and a professional.
It is also worth using social media’s privacy settings so the University or a potential employer could be less likely to see your posts. Some employers do look up potential candidates online, so whatever you post they may also see.