The latter. Basic logic says that if one entity arrives at the point where they’re ready to execute him, they’ll execute him. If the state declines to execute him for any reason (still being appealed, sentence commuted, he was never up on state charges in the first place, etc.) that doesn’t make him immune from the Federal sentence, whatever it is. It just means he won’t be executed twice.
I don’t think it’s that simple. In the case referenced by the OP, the charges stem from the same incident, but in a case where a defendant is being tried for discrete crimes - say, two otherwise unconnected murders - the first sentence (and possibly even sentencing) would be stayed pending the disposition of the second case.
That said, I’m unable to find a case at the moment in which this scenario occurred.
To be exact this is what the court has said (or not said) about executing an innocent person:
“[T]his court has never held that the Constitution forbids the execution of a convicted defendant who has had a full and fair trial but is later able to convince a habeas court that he is ‘actually’ innocent.”
As a constitutional matter, Scalia’s assertion is not wrong. The court has never found a constitutional right for the actually innocent to be free from execution.
The Court did rule in 1993 that a claim of innocence did not prevent the state from executing an innocent person. It left open the question of whether an innocent person could be executed.
It has also never ruled that it has. Apart from anything else, there’s no reason for it to; courts are finders of fact, and a defendant found to be innocent won’t be executed. A defendant found to be guilty upon final appeal is, as a matter of law, not innocent.
This is also annoying because it’s a pretty simplistic analysis of the case that misses several major points.
We have a system that takes what we believe are appropriate steps to prevent an innocent person from going to jail. To do this, we let a lot of guilty people go free. There’s no question amongst anyone informed and sane that in fact, we do let more guilty people go free than put away innocent people.
At some point, we have to determine that our methods of detecting guilt and innocence are good enough. If we aren’t allowed to execute anyone who claims they are innocent, we aren’t going to have any executions. If we can’t put people who might possibly be innocent in jail, no one will go to jail. I’m sure every person sentenced to death, “actually” guilty or not, has/had a person who was convinced they were innocent.
What the court has said is that it’s not going to throw out the tenets of our system and throw every single criminal disposition into doubt now and forever. We’re not interested in litigating every case hundreds of times.
And your restatement of the point is simply incorrect. An innocent person does have the right not to be executed. No innocent person can be given the death penalty, since that requires them to be found guilty. The question is the same: what process is good enough that we can call it fair? Ours is pretty close to fair. It has problems, but it works decently well.