Whenever an action is somewhat complicated, performing the action almost never is unintentional. However, when not performing the action, intentionality may vary - you may have forgotten or otherwise failed to carry it out, or you may have decided not to do it at all, and as a third option, you may not have had any intention whatsoever. Thus, for a large number of actions, it seems more likely that conveying volition would be more natural and more necessary in the negative than in the positive.
What ways could such a distinction be encoded? There's a lot of them, really!
One way could be lack of person marking on verbs for the negative whenever volition is lacking; another could be different constructions altogether - something like English or Finnish for volitional negativity, something with just a negative particle for volitionless negativity. Yet another option could be negativity concord on objects and the like with volitional negativity.