Suppose two people, A and B, are accused of some criminal activity, and the court decides that A is to blame, while B is blameless.
Now, suppose that A knows that B is the one to blame, while he is innocent, and appeals. (B does not participate in the appeal because he was found innocent)
Suppose the court agrees and decides that B was the crime's actual perpetrator and removes the blame from A. Could they both be set free?
An appeals court does not re-try a case, so you cannot appeal a case just because you know you are innocent. You can appeal a case for various technical flaws in the original case, for example the court plainly made an error in applying the law, the law is unconstitutional, the prosecution was corrupt in certain ways, or there was in fact insufficient evidence to sustain a conviction. Appeals courts do not generally consider new evidence
If you discover new evidence, you might be able to file a petition for a Write of Actual Innocence. The court would not "decide" that B was the perpetrator, but they might agree that A is innocent. Since B has previously been found not guilty, B cannot be tried again, so he is not in jeopardy (because of the double jeopardy clause).
The answer would be different in a jurisdiction like Gabon or Italy, which have different legal systems from the US.
You would have got a different answer if you had asked this question of an English lawyer about a trial at the Old Bailey in London.
In England, the old distinction between a minor offence ("misdemeanor") and a serious offence ("felony") was, in theory, swept away in 1971. But in reality, the distinction survives (slightly modified), albeit no longer with those names.
In terms of the appeals procedure, the difference may still be significant. Offences so minor as to be misdemeanors are no longer tried before a jury, and the right of appeal is extremely limited. For these offences, triable only before a Magistrate, there is normally only a fine on conviction, or a prison term not exceeding 6 months.
For a more serious charge, the right to a Jury trial is either automatic or is exercisable at the option of the accused. Where the trial is by judge and jury, the jury decide his guilt or innocence; and, because of that, an appeals court will usually (except in rare cases) refuse to substitute its own view of the facts for that taken by the jury.
The appeal court normally only deals with procedural issues, of which by far the most common is the type of application based on (some variation of) the allegation that the judge misdirected the jury. The accused then attempts to find some fault with the procedures which the judge adopted (perhaps alleging some procedural unfairness), or with his directions to the jury about the law.
In terms of shifting the blame from one defendant to another, this is relatively unlikely. The appeal court does not hear any evidence at all. It only considers legal arguments, and these generally pertain not to the evidence at the original trial, but usually only to the procedures used. If matters of evidence do arise, they might take the form of an objection to the judge's decision as to whether or not to permit a particular witness to give evidence (most commonly arising in relation to whether an expert was suitably qualified to give evidence).
In English law, the law of criminal evidence holds that a person cannot be convicted on the uncorroborated testimony of an accomplice. This most important restriction prevents any possibility of there being an attempt by one defendant to cast the blame onto another, at any stage in the proceedings.
The principal difficulty for the co-defendant who was acquitted at the trial is, in the event of an appeal against conviction by another defendant, that the double jeopardy rule was abolished by the last Labour government (i.e. fairly recently), and there have not (yet) been enough high-profile miscarriages of justice reported to have caused it to be restored.
You don't state a jurisdiction, but at least in the US, there is a distinction between questions of law and questions of fact. The trier of law decides the former, while the trier of fact decides the latter. The trier of law is the judge, and in a jury trial the jury is the trier of fact (in a bench trial, the judge serves as both trier of law and of fact, but those roles are still distinct).
So let's say Person A is charged with murder, and the prosecution presents a witness who testifies that Person A confessed to them, and the defense objects to the testimony. Whether the testimony should be allowed is a question of law. Whether the testimony is true is a question of fact. So if the judge decides that the testimony should be allowed, then it's up to the jury to decide whether to believe the testimony.
If you disagree with a judge's ruling against you on a question of law, you can file an appeal. You are appealing the ruling, not the verdict. If you are convicted of a crime, you can't appeal the verdict, you can only appeal the rulings by the judge that led to that verdict. In an appeal, you can ask the appeals judge (or judges), as a trier of law, to overrule the trier of law (judge) in the original case. But you can't ask them to overrule the trier of fact (jury). Those are separate roles. If the appeals court agrees with you that the original ruling is wrong, they may decide that the verdict was improperly arrived at. But they won't rule on whether or not you are guilty; they aren't acquitting you, they are simply invalidating the original determination of guilt, and leaving the question of your guilt legally undecided. They certainly won't declare that some other person is guilty. Only a trier of fact can do that. Now that there is no determination of fact, the prosecution can, if they want, then schedule a new trial, conducted according to the appeals court's ruling on matters of law, and try to convict you again.
So if Person A is convicted and Person B is tried but acquitted, and an appeals court throws out Person A's conviction, and Person A is tried again and acquitted, then yes, both would go free, as Person B (barring issues such as dual sovereignty) cannot be tried again, as that would be double jeopardy.
