I think the sentence basically means that we need to consider the man's history to judge if something is good or ill fortune to him.
I agree with you on this. This seems to be the meaning of the sentence, especially considering the example given in the paragraph that follows your quote.
I also think the relevant part of it can be shortened as "good or ill fortune has a person identified by...". If I'm right, then what does "have someone identified by" mean in this context?
I disagree. It would break the meaning of the sentence. The broken sentence could be read two ways.
In English, the construction "to have something/someone + past participle + by" is often used in sentences such as this:
John has his car cleaned by professionals. (okay)
Ill fortune has a person identified by his history. (what? O_o)
This would be hard to apply to your example sentence. Ill fortune cannot command a man's history to identify this man. "History? It's ill fortune calling. I need you to identify one person for me."
The second way to read it would be similar to reading this sentence:
A poet has a cat (which is) identified by its black tail. (okay)
Ill fortune has a person (who is) identified by his history. (what? O_o)
See, "good or ill fortune" cannot have a person in this way.
The real meaning of
It therefore seems to me worth exploring the position that most good and ill fortune has as its subject a person (who is) identified by his history and his possibilities
is that the subject experiencing some event is a person whose characteristics include all the circumstances of his life up until this moment. This person is "the subject of ill or good fortune". This person is idendified ("described") by his history and his possibilities.