Responsibility (literally the ability to respond) can be regarded as your skill to respond appropriately to each situation you meet, moment by moment.
We tend to regards people as responsible when they behave relevantly in most situations. The social idea of your being responsible for some future event needs careful appraisal. If this means you intend to do all you can to ensure it happens as planned, this may not be harmful. However, the moment you or others, regard yourself as guaranteeing some future outcome, this is impossible, since the future is unknown and cannot be guaranteed. In this case mental stress is probably inevitable. Many things, most of them unknown to you and uncontrolled by you, affect future events, and it is worth remembering that it is not you that even controls your mind’s thoughts or your body’s behavior. The Tibetans clarify it:
I think what I think.
I do what I do.
What happens, happens.
One aspect of real, possible, responsibility is recognizing clearly what is real and what is not, so that your actions naturally more closely stem from reality and so are likely to be more appropriate.
This way there is likely to be more benefit and less harm resulting from your thoughts, speech and actions. Accessing the unconditioned mind, pure awareness, often, encourages the habit of natural presence to what is happening. This may be you best way to become more responsive and responsible, an essential component of kindness and your peace of mind and happiness that flow naturally from these.