What is the appropriate action for someone burdened by debts, who is currently unable to repay them, especially given a large family and compelling circumstances?

The fundamental principle is the obligation to grant respite to the one in hardship, based on Allah's saying: "And if there is one in hardship, then [let there be] a postponement until [a time of] ease. But if you give [it in charity] as a donation, it is better for you, if you should know." The questioner is advised to fear Allah and to avoid usury, and to sincerely intend to fulfill the rights of people, as the Prophet (peace be upon him) said: "Whoever takes people's money with the intention of repaying it, Allah will repay it on his behalf; and whoever takes it with the intention of destroying it, Allah will destroy him." He should frequently recite the reported supplications for settling debts, and he is entitled to receive from zakat (definition) to pay off his debt.