Is it permissible to give the Sadaqah to another family if the family specified by the giver has improved its condition, and it is no longer possible to communicate with the giver?

You are not permitted to spend the money on anything other than what its owner specified. The obligation is to spend it on the designated family. If you violate this, you become liable for the money until you deliver it to its rightful recipients, for Allah the Almighty says: "Indeed, Allah commands you to render trusts to whom they are due."