In my understanding, consequentialism doesn't accept a moral distinction between sins of omission and sins of action. If a person dies whom I could have saved through some course of action, I'm just as guilty as I would be if I murdered the person. In my view, there must be a distinction between murder (=causing a death) and failure to prevent a death.

If you want to be more formal, here's a good rule. Given a death, would the death still have a occurred in a counterfactual world where the potentially-guilty person did not exist? If the answer is yes, the person is innocent. Since lots of poor people would still be dying if I didn't exist, I'm thereby exonerated of their death (phew). I still feel bad about eating meat, though.