In every family, in every team, in every group there will be someone who is least tolerant of messes, unfinished tasks, and unaddressed problems. That does not mean that that person is a "neatnik" or even extremely responsible. Just as within companies who just don't think they can live without ranking their employees, it is always within a range. For employee ratings, the "low end" might be someone in the top 5% of the population while others are in the top 4%. In the case of responsibility, it may mean that, for that person, the "straw that breaks the camel's back" is when there are 34 unwashed socks scattered across the floor rather than 40 unwashed socks (or an infinite number of unwashed socks).
In the above cases, the responsibility is self-assigned. It is self-assigned because the person's characteristics are such that leaving the tasks not done causes greater inner turmoil than any efforts needed to take care of the problem.
It is all relative. But responsibility includes assuming the duties of resolution of a problem. Those that recognize, and cannot stand to continue, a problem first will be the first to try to resolve the problem. They scoop up all of the unwashed socks and put them into the clothes washer (hopefully they also add detergent and turn it on). They pick up that book left on the floor that everyone keeps carefully stepping (or not so carefully, sometimes tripping) over.
Responsibility is also closely tied to reliability. Responsible implies that you have authority, and will be held accountable, for what you are supposed to do. Reliability says that if you say you will do something then, if at all possible, you will do such. A person can be reliable without being responsible because a person can do things for which they have no authority or accountability. It is difficult to imagine making someone responsible if they are not also reliable. It would be a scenario of planned failure -- giving authority and accountability to someone who is unreliable.
As is true of almost all internal change -- it cannot be imposed from without. There has to be a desire, within a person, to change. Thus, someone who is not responsible is not likely to become responsible unless something occurs to make them want to become responsible. Although there are non-military situations that force individual improvement and responsibility within the group -- there are more examples of such, in our society, within the military.
In the movie "An Officer and a Gentleman", the character played by Richard Gere -- Zack Mayo -- is used to floating along, grifting, taking the easier paths. But his goal of feeling self-worth and belonging is a sufficient motivation for him to choose to change. This is the purpose of "tough love" -- creating a situation within which a person can choose (or not choose) to change. In the movie, it is either change or eviction from the military. In a family, the penalty may be eviction from the family support network. Personally, I think the latter is the harder to execute as the military already is structured with its firm rules and required behaviors. But, in either case, the change may be pressured from without but it must be the choice of the person to change.