John Locke came up with the original "Frankfurt-type example". (The examples have been called "Frankfurt-type examples after Harry Frankfurt's ingenious development of them in a 1969 Journal of Philosophy paper, "Alternate Possibilities and Moral Responsibility."
Here is Locke's version. A man is asleep, and while asleep, he is transported into a room. When he awakens, he thinks about leaving the room, but he decides (based on his own reasons) to stay in the room. Unbeknownst to him, the room was locked, and thus he could not have left the room. Locke did not say that the man stayed in the room "freely," because Locke held that acting freely entails freedom to do otheriwse. But he did say that the man voluntarily stayed in the room, although he could not have left the room.
In Locke's example, the fact that the man could not have left the room plays no role in his practical reasoning or behavior. It thus seems irrelevant to his moral responsibility. I would say that the man can be held morally responsible for staying in the room, even though he could not have left the room.
Now of course the man could have chosen to leave the room, could have tried to leave, and so forth. So (apart from any special assumptions, such as God's omniscience or causal determinism) he did in fact have SOME alternative possibilities. Harry Frankfurt seeks to expunge even these alternatives, envisaging an agent, "Black", who can control even the poor man's brain, anticipating his choices in such a way as to render it true that the man could not even have chosen or tried to do otherwise.
The "Locke/Frankfurt" examples have become a template for testing the relationship between moral responsibility and the sort of freedom or control that involves alternative possibilities. I agree with Locke and Frankfurt; in my view, one can choose and act freely, and thus exhibit the kind of control that grounds moral responsibility, without having freedom to choose or act otherwise. I have thus defended an "actual-sequence" approach to moral responsibility. But this is highly contentious. What do you think?