Our Gemara on Amud Aleph discusses situations where if a father violated a prohibition of Chol Hamoed, and is fined by the rabbis by being forbidden to get benefit, are the sons who inherit the father also subject to that penalty?

We must first ponder, why should the sons be held accountable for their father’s misdeeds? Rashi offers a simple explanation: If the father were still alive, his possessions would be subject to the penalty, and thus the children would automatically be affected. If so, his possessions still have that valence after he dies. Looking at it this way, it has nothing to do with the intent of the penalty, rather just a technicality. 

One might argue that there is a different idea, perhaps the rabbis extended the penalty to the children out of the same motivation as the penalty of the father, to act as a deterrent. I think Rashi did not find that peshat acceptable because it counters the sentiment of the following verse:

Devarim (24:16)

לֹֽא־יוּמְת֤וּ אָבוֹת֙ עַל־בָּנִ֔ים וּבָנִ֖ים לֹא־יוּמְת֣וּ עַל־אָב֑וֹת אִ֥ישׁ בְּחֶטְא֖וֹ יוּמָֽתוּ׃ 

⁦Parents shall not be put to death for children, nor children be put to death for parents: a person shall be put to death only for his own crime.

(Although the derash on this verse refers to sons testifying about their father (Sanhedrin 27b), the pashut peshat is about punishment. See Hekesav VeHakabbalah on this verse for a full discussion.)

While we are on the topic, let us explore some the Jewish theological ideas about children bearing the sins of the fathers.

This is in regard to matters of earthly court, however in regard to the heavenly court other factors apply:

Shemos (20:5)

פֹּ֠קֵד עֲוֺ֨ן אָבֹ֧ת עַל־בָּנִ֛ים עַל־שִׁלֵּשִׁ֥ים וְעַל־רִבֵּעִ֖ים לְשֹׂנְאָֽ֑י׃

visiting the guilt of the parents upon the children, upon the third and upon the fourth generations of those who reject Me,

If the children follow in the evil ways of the father, they then are liable for the sins of the father as well. (Rashi Op. Cit., and Berachos 7a)

Also small children seem to still fall under the father’s fate, see Rambam, Laws of Teshuva 6:1:

There is a category of sin for which justice demands that punishment should be visited upon the sinner in this world, on his body, or his property, or on his infant children, for the little children of man, who have not yet reached the age of intelligence nor attained the age when they are included among those who are obliged to observe the precepts, are considered man's own acquisition, even as it is written: "Every man shall be put to death for his own sin" (Deut. 24.16)—he suffers for his own sins when he reaches the age of man.

Rambam’s formulation makes sense when you think about it because children in almost all ways are captive to the decisions of their parents. Where they live, what foods they eat, and what they are taught all originate with parental choices and only later can the child evaluate and take responsibility for his or her choices.

A fun fact about this verse is that it is one of the few verses in the Pentateuch that is referenced in the writings of the prophets. In Kings II:14:6 Amatzyahu refrains from executing the sons of those who successfully plotted and assassinated his father, which would have been customary in a typical political purge:

⁦But he did not put to death the children of the assassins, in accordance with what is written in the Book of the Teaching of Moses, where the LORD commanded, “Parents shall not be put to death for children, nor children be put to death for parents; a person shall be put to death only for his own crime.”

Even more fascinating is Yechezkel chapter 18, which is essentially a chapter long expansion on the ethics of this verse. Yechezkel’s message to the Jewish people is that there shall be no legacy of sins, and the righteous son of an evil father, or an evil son of a righteous father will bear their own rewards or consequences. Yechezkel goes on to say that the person who repents is also no longer liable for his sins of the past. 

The Torah’s ethics, here as in many halachos, were revolutionary and ran against the tide of contemporary conceptions in the ancient world. We are so used to individual rights as a given, that we can hardly conceive of a different value system. However, in the ancient world, families and bloodlines were held to group accountability and could easily be executed for a relative’s disloyalty or treason. The Torah awakened in mankind a new kind of justice, where individual judgment, choice and autonomy became the supreme value and not collective punishment. This surely seeped into the secular awareness through the Bible and led to the various human rights revolutions of the 18th century, culminating on that almost divine document, the Declaration Independence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.