Philippa Foot is most known for her invention of the Trolley Problem thought experiment in the 1960s. A lesser known variation of hers is as follows:
Suppose that a judge is faced with rioters demanding that a culprit be found for a certain crime. The rioters are threatening to take bloody revenge on a particular section of the community. The real culprit being unknown, the judge sees himself as able to prevent the bloodshed from the riots only by framing some innocent person and having them executed.
These are the only two options: execute an innocent person for a crime they did not commit, or let people riot in the streets knowing that people will die. If you were the judge, what would you do?
Moral responsibility initially lies in the people responsible for creating the situation. The rioters are responsible regardless of which choice is made because they are the ones creating the circumstance in which there is no option to avoid injustice. If you're the judge, you're not responsible for the rioters killing more than one person, however unfortunate that is. You would be responsible for knowingly killing a known innocent.
Likewise, with the trolley problem, regardless of what choice the operator makes, whoever tied up the people and put them on the tracks and whoever caused the trolley to barrel out of control is at least initially responsible.