"As well as" would be more idiomatic English than "besides".

I think the line length needs to be checked here.

"... that we will encounter..."

I find the original language here rather hard to parse because the concepts are quite unfamiliar (a loop that terminates through exhaustion of an iterable...).

Perhaps:

A for or while loop can include an else clause.

In a for loop, the else clause is executed after the loop reaches its final iteration. In a while loop, it's executed after the loop's condition becomes false.

In either kind of loop, the else clause is not executed if the loop was terminated by a break.

exemplified in

This just seems bad. You restricted it to for statements, but it also applies to while statements. And the else clause isn't really "extra" (I even checked some dictionaries, they all defined it like "added to an existing or usual amount or number; additional. Example: they offered him an extra thirty-five cents an hour". And loop statements can only have one else clause.)