While we'll touch on this later in the article, under certain circumstances, a big bad of a story can certainly have a redemption arc. Whether or not this arc makes sense and is done well falls down to various factors such as (but not limited to); their acts, personality, goals, and how they are written or portrayed. In short, it vastly depends upon the character and the story - and more specifically what their redemption would mean for the overall plot and the impact their redemption may have on other characters.