Responsibility is a learned discipline. The teacher may be parents or peers, bosses or coworkers, friends or enemies, a formal or informal teacher, but responsibility must be taught and learned. The affect irresponsibility has on a life, a community, a business or a nation is cataclysmic. Conversely, a strong sense of responsibility is needed to grow any family, business, government or nation. Bluntly, if there is an issue or problem those who are irresponsible are part of the problem while those with a firm, learned understanding of responsibility or part of the solution.
My father, a First-Sargeant in the US Air Force for 20 of his 30 years, never used the word "priority". He used the word "responsibility". It was not he did not prioritize. He most certainly did. He refused to look at a responsibility as anything other than demanding completion.
When told to "take responsibility" for one's work the expectation is to take ownership for one's work. How many people do you know who own a house and don't take care of it? Or a car? Or a child? The evidence of how someone does their work will tell you how they take care of other things. One part of this responsibility is being aware of what needs doing, what hasn't been done, and what could be done. Responsibility is not limited to maintaining but includes creative innovation in making the job or the work more efficient and better. Responsibility raises the bar.