I believe the general grammar for 「ないことはない」 means "can; it is not impossible". However, I am having hard time trying to translate this example sentence:
「どうしても話してくれと言われれば、話さないこともない。」
Mostly I cannot figure out who the subject is. My tentative translation is "You can speak if you are asked to do so." Pretty sure this is not correct and would be grateful for a more accurate translation!