Are the children held accountable for a debt their father incurred in their name, but from which they did not benefit, and which the father did not repay, and they do not possess the money to repay it?

The matter has details: If the father took out a debt in the son's name and benefited from it without the son's permission, then the father alone is obligated to repay it. If he does not repay it despite being able to, he is exposed to Allah's punishment on the Day of Judgment, unless it is repaid from his inheritance or the creditor pardons him. However, if the father took out the debt with the son's permission, then the son is obligated to repay it if the father does not, because he is, in effect, the guarantor. Considering the observance of the father's right, repaying the debt on his behalf is a great act of devotion for someone who is able.