what are 2 offenses for which a person's failure to act will constitute an offense?

Answer 1

There are far more than just two.

Failure to act -- an omission -- will constitute a willful act where the failure to act is knowing, and where there is a duty to act.

A duty to act may arise out of statutory requirement -- such as a statute that requires people to clear a certain area around their homes to prevent fire damage -- or where there is a special relationship -- such as the guardian of a minor child or a dependent elder -- or where there is a professional obligation -- police or attorneys, for example ....

And a duty to act may arise if the defendant caused the problem which resulted in the harm, or intervened and made the situation worse than it would have been if they had never intervened.

Any of those may create a duty to act, which can result in a knowing omission (willful failure to act) being punishable, either in tort or as a criminal offense.

Answer 2

How about ignoring a summons for jury duty and, how about aiding a fugitive?

Answer 3

paying taxes and being born a black male