What is a word that means "to be unaware of responsibility" or "to not realize there is a responsibility to take"?

Solution 1:

Like @Anton, "oblivious" also came to mind for me, but I also like:

nescient: lacking knowledge; ignorant; agnostic (Collins dictionary)

Or, for a tint of darkness:

benighted: lacking cultural, moral, or intellectual enlightenment; ignorant (Collins dictionary)

Solution 2:

Three words come to mind, all close to your need but perhaps dependent on context.

heedless = If you are heedless of someone or something, you do not take any notice of them

Collins dictionary

oblivious = not aware of or not noticing something, especially what is happening around you

Cambridge dictionary

remiss = not doing a duty carefully or well enough

Cambridge dictionary

My favourite is heedless. So we might say "She was heedless of duty, of responsibility, and of the needs of others."