A word for "negligence of duty or responsibility"

Solution 1:

The words you're looking for are:

dereliction (of duty)

From oxford:

The shameful failure to fulfil one’s obligations

As in, "the prosecution team were guilty of dereliction of duty for failing to disclose evidence"

and derelict

From oxford:

chiefly North American Shamefully negligent of one’s duties or obligations

EDIT: Although derelict does have other meanings, as noted in the comments.

Solution 2:

In less formal conversation, a person "shirks" his duties, and is called "a shirker".

Oxford definition:

Avoid or neglect (a duty or responsibility)

As in, she has not shirked her duty, nor shied away from pain.

Solution 3:

I agree with Tushar - dereliction (of duty) - fits best here.

I just wanted to add that Delinquent is a (sometimes pejorative) adjective or noun most often used to refer to a teenager/young person who does not engage in normal education/training/work appropriate for their stage and may use their time to cause trouble instead. - so I would not use Delinquent in this context, unless you want to describe a young person who has issues with the whole of their life.... ...dereliction of duty normally refers to one individual action - so that there may be one particular task that is not done properly or one area of responsibility that is overlooked.