Dear Sanjana,
Though you have raised a question on your safety, first let me give my different take.
The day before yesterday, two employees fight at the workplace. Today, they have been terminated from the service. Why such hurried termination? Workplace fights or even physical assaults happen occasionally. Does it mean that your organisation should have given short shrift to the due process of law?
You (means your company) could have suspended these two employees and domestic enquiry should have been ordered. The Enquiry Officer (EO) should have investigated the incident as to what was the cause of the eruption of the fight. Many times the domestic enquiry goes on for several days. This helps in shifting the attention from HR to the EO. In fact, many times EO is hired from outside. This also helps in making the enquiry impartial. With hasty termination, the terminated employees might have perceived that they have been terminated because of HR. Their perceptions may be wrong but the one who is at the front always bears the brunt.
The enquiry would have helped you in understanding whether there was a system's flaw but you ended up punishing the people. By the way, when the fight ensued, where was the Manager? Why he did not step in to control the fight? What was his/her role in preventing the fight?
If one of the fighting employees demonstrated behaviour that bordered on criminality then why he was allowed to work at all? He could have been terminated by giving him some sweet poison. Take the meaning of "sweet poison" figuratively and not literary. The cause of the incident could be the lack of this foresight also.
Now coming to the solution. As the learned member Mr Umakanthan M has written, that one of the fighting employees could be hostile towards you could be just your perception. Yes, terminated employees do bear a grudge against HR. However, physical harm is a remote possibility. If at all if he were to take revenge then he should take it against his opponent with whom he had a fight. Therefore, you may not
tilt at the windmill.
Take precaution for the next few weeks. Be vigilant while commuting to the office. Keep a pepper spray with you and observe all the rules of self-defence.
Thanks,
Dinesh Divekar