Well, in headlines, they try to pack in as much information as possible, so they leave out prepositions, articles, and “to be”. In an actual sentence, we can use “reduced relative clauses” (you can search that term for more info): Relative clause: Police questioned Mr Jones, the man who had been arrested at the scene of the crime. Reduced relative clause: Police questioned Mr Jones, the man arrested at the scene of the crime. I would say that if the reduced relative clause is perfectly understandable, you should use it. It’s good style never to use more words than necessary for clear communication.

They are both used in different contexts: 1- The man arrested yesterday is in jail now (it's the equivalent of saying: the man who was arrested yesterday is in jail now) 2- The man was arrested yesterday (an event that happened in the past, i.e. the actual arrest) 3- This man is arrested for murder (his current status, i.e. being arrested)

Man killed. Man was killed. Man, I killed it last night. Man is killed. - Nono. but... In the event that that man is killed by your action or inaction, you are going to get arrested. - Ok.