How would you classify the words "how" and "come" when they are used in questions, such as "How come you bought that book"? The meaning and structure is similar to "Why did you buy that book", but there is a significant difference. The phrase "why did" is a typical Adverb + Auxiliary Verb combination. It could be replaced with any other combination, e.g. "When will", "How could", "Where can", etc.
The word "come" cannot be considered a main verb. It cannot take a subject. It cannot be an auxiliary verb either because it has no effect on the form of the main verb. We can use any tense and aspect in "how come" questions, e.g. "How come you have been avoiding me". vs. "Why have you been avoiding me".
I think the phrase "how come" is similar to phrases that we use for suggestions and short elliptical agreements. For example, the phrase "how about" in "How about we eat dinner together" and the words "too" and "neither" in "me too" or "me neither". I think these words and phrases are all disjunctive adverbs. They follow the pattern Disjunctive Adverb + Clause / Disjunctive Adverb + Noun Phrase / and Noun Phrase + Disjunctive Adverb.
Disjunctive adverbs normally modify entire clauses, as opposed to predicates, e.g. "Frankly", "By the way", etc.