He could have died.
This could/can mean two things [maybe more]
"It was a possibility, but it didn't happen"
OR
"There is a possiblity that he died but I don't know".
He might have died.
This could also mean two things [maybe more]
"We don't know what happened, but there is a SMALL possibility that he died"
OR
it can be used as an admonishment,
"How could you kids be so stupid as to try that stunt?" He might have died.
'may' can also be used in this fashion to admonish; "he may have died" but it is much less likely that either 'might' or 'could'.
In pure speculation, ie. when these modals are used as epistemic predictors [modals of certainty], when we use 'could', all we say is, "There's a possibility but my 'could', in and of itself, doesn't state how strong a possibility.
'Might', on the other hand, confines the range of possibility from a miniscule to a small chance that something happened, will happen, is happening now, or happens all the time.
++++++++++++++++++
In BE, the following would be used:
1- He might have died. (he survived an incident where there was a possiblility of dying)
2- He may have died. (we don't know whether he has died or not- he's missing up a mountain in a storm, say.)
However, the distinction is being eroded and many people now are using 'may' for the fisrt meaning.
That's what some believe but it's simply not how English works, Tdol. In a purely epistemic sense when modals are being used to describe differing levels of speaker certainty, the only difference between 'might' and 'may' is that 'might' shows a speaker who is less certain.
1- He might have died. (we don't know whether he has died or not- he's missing up a mountain in a storm, say.)
Lower level of certainty than 'may'.
2- He may have died. (we don't know whether he has died or not- he's missing up a mountain in a storm, say.)
A higher level of certainty than 'might'.
[An even higher level of certainty becomes, "He probably has died", and an even higher level, "He almost certainly has died" which under the right circumstances, could morph into "He must have died".]
This distinction that some feel is being eroded has actually never existed. The people who think that's the case are confusing epistemic modal meaning with deontic modal meaning.
As the old saying goes, you've gotta compare apples to apples.