He may have died in the accident - possible, probability. I don`t really know
He might have died in that accident if he hadn`t been saved in time. - If I use this sentence in this way, I understand exactly the speaker`s message
If I say:
He might have died in that accident - the meaning or the message is quite ambiguous; the speaker must come with more explanations or , otherwise, I may understand the message in my own way: he might have died in that accident but he didn`t die because...- and I say the reason why he is still alive or, simply, I don`t know what happened to him after the accident.