Sanhedrin, Chapter 9, Mishnah 5. This Mishnah deals with a very unusual case, where we are also dealing with a person who is ultimately killed - but only passively, as we will see shortly.
The first case - someone who was lashed and repeated the offense:
This refers to a person who committed a sin for which the punishment is kareis. This does not mean a sin punishable by death at the hands of the court, but rather a sin that carries at least kareis - and these prohibitions are extremely severe. If he had transgressed inadvertently, he would have brought a chatas offering; but this person did so intentionally, in the presence of witnesses who warned him not to do so, and nevertheless he did it - and therefore he receives lashes.
The meaning of kareis is an early death, and as the word itself implies - to be cut off: he is seemingly cut off from the World to Come, meaning that this person has already lost his right to live. Nevertheless, the Torah gives him an opportunity to repent. However, this person did not repent: he committed the exact same sin a second time, was convicted and lashed again, and even went back and committed it a third time, with witnesses and a warning, completely ignoring the consequences of his actions.
It must be emphasized that this is not a person who committed two different sins - such as eating a kezayis of blood one time and a kezayis of cheilev another time. This is not the case: this person ate cheilev, was warned and ate it, and was lashed; he was warned again, and was lashed; and now he has done it a third time. Since he already lost his right to live due to the punishment of kareis that he previously incurred, he is not given a third chance.
In the words of the Mishnah: "Beis din machnisin oso lakipah" - the kipah is a very narrow and closed space, like an especially cramped prison cell. The court does not kill him, but rather leaves him to die passively, or if you will, lets him kill himself: "Ma'achilin oso se'orim" - they feed him barley, and after he is very hungry and eats it, the barley causes his stomach to burst, "Ad shekriso nivka'as" - until his stomach bursts, and he dies from this.
The second case - one who kills a person without witnesses:
Similarly, a person who committed a crime - and here we are speaking specifically of the crime of murder. Unlike other cases of those liable to death at the hands of the court, where we look for any technical flaw in the world to exempt the accused, here we are dealing with a situation where the court knows with absolute certainty that the person is a murderer, but there is a technical problem preventing his conviction - such as the witnesses disagreeing on a small and irrelevant detail.
The Rambam explains that murder is the most destructive and harmful anti-social action that exists, undermining the very fabric of society, unlike other types of sins. Therefore, even though in other sins a technical detail would result in the person going free, regarding someone who is known to be a murderer and there is a technical flaw preventing his execution - we do not execute him, but we leave him to die.
And how is this done? "Machnisin oso lakipah" - they place him into that same narrow cell, "Uma'achilin oso lechem tzar umayim lachatz" - they give him very little food, a little bread and a little water, until he becomes very hungry, and then they feed him barley bread like in the first part of the Mishnah, which causes him to swell up and die from his stomach bursting.
This is indeed a terrible death, but the point is that the court does not kill him directly. In reality, he kills himself, and the court merely allows the process to happen much faster - but they do not execute him with their own hands.
In summary: In this Mishnah, we learned of two cases where the accused is placed into a kipah: someone who was lashed and repeated the same offense that carries kareis, and someone who is known to be a murderer but cannot be convicted due to a technical flaw in the testimony. In both cases, the court does not put him to death with their own hands, but rather brings the accused to die in a passive manner.