He may have died in the accident.- current status unknown
He might have died in the accident.- he survived, but there was a risk of death
However, this distinction is being eroded and many speakers use 'may + have + past participle' with the second meaning.
This distinction never existed, Tdol, at least not in the sweeping fashion that has been suggested. In certain circumstances, 'might' can be used in a mocking, admonishing type fashion;
"He might have been killed if you two had tried that stunt."
But to suggest that a speaker can't state that, in their mind, there's a greater certainty that death could have occurred, leaves certain thoughts unexpressable in English. This is something that just can't possible occur.
"He may have been killed if you two had tried that stunt."
"He probably would have been killed if you two had tried that stunt."
"He almost certainly would have been killed if you two had tried that stunt."
"He would have been killed if you two had tried that stunt."
He may have died in the accident.- current status unknown or an admonishment
He might have died in the accident. - current status unknown or an admonishment