The name of this grammar structure

It is a serious, and sometimes fatal, disease that may become epidemic in crowded, unsanitary living conditions.

I'm trying to find the name of grammar structure (a very technological term, not just something like "parenthetical phrase to add additional information", as I seek to find every information about it) of "and sometimes fatal", a parenthetical phrase and what seems to be a coordinative adjective.

I just do not understand how it is grammatical to wrap that conjunction and adjective in commas like that. Isn't comma supposed to come before the conjunction only when a new independent clause is beginning?

Solution 1:

It is called a "parenthetical phrase." While you state that is not the name you are looking for, that is the grammatical term for it. More specifically, and within the subset of parenthetical phrases, it is called an "aside." Basically, you are more right than you imagined, more on the right path than you seem to have thought.

Solution 2:

Would you be happy with: '... a serious (and sometimes fatal) disease ...'? The comma is actually a tiny parenthesis. Since they are represented in speech by a pause, '(' and ')' sound the same (and aren't apparent at the beginning or end of a sentence).