Is it permissible to agree that one of the partners will undertake all the work independently and receive the full wage, in exchange for 500 Riyals for the other, and how would a claim be made in the event of a loss?

Your friend relinquishing his right to work for you, or your relinquishment of it to him for a specific sum, falls under the category of selling intellectual property rights. There is no harm in this, as these rights hold value just like material rights. Whoever purchases an intellectual property right bears the loss alone, and the seller bears no responsibility.