It is an example of a nominative absolute construction - it is a construction that has a сlose semantic connection with the rest of a sentence, although gramatically not connected with this rest of the sentence with any means. It is always separated by a comma from the rest of a sentence.
This construction always has a subject, after which there is always a participle or an infinitive.
For example, in your sentence:
The character was intentionally designed to be very charismatic and articulate, his main source of fear being derived from his warped sense of reasoning.
The subject of a nominative absolute construction (in bold) is "his main source of fear" and participle is "being derived".
Sometimes, when a participle in a nominative absolute construction is "being" after which subject complement takes place, the "being" can be omitted. For example, your sentence
His features contort with obvious pain as he tells his story, his memories of Caroline clearly something he holds precious.
is a shorthand for
His features contort with obvious pain as he tells his story, his memories of Caroline being clearly something he holds precious.