What is the ruling of Islamic law on a family that relies for its sustenance on stolen money, knowing this, and having no other source of income?

Theft is one of the gravest sins, and its earnings are among the foulest. It is an assault on the rights of others. Sustenance from unlawful sources prevents the acceptance of supplication and corrupts the soul. The thief and their family must fear Allah and ask Him of His bounty, so He may open doors of provision for them. For, "And if only the people of the cities had believed and feared Allah, We would have opened upon them blessings from the heaven and the earth," and "And whoever fears Allah – He will make for him a way out and will provide for him from where he does not expect."