I understand your predicament. As per Saudi Arabian Labor Law, an employer has a set of obligations towards the employees.
According to Article 41 of the Labor Law in Saudi Arabia, the transfer of a sponsorship can happen in two ways:
1. Upon agreement of both parties (the current and the prospective sponsor).
2. By an order from the Ministry of Labor.
If your current sponsor (kafeel) initially agreed to transfer your sponsorship to a new employer but is now refusing to do so without a valid reason, you may file a complaint with the Ministry of Labor.
Article 13 of the Labor Law states requires the employer provide suitable housing for all of his workers if the latter are not provided with such housing in accordance with the terms of other regulations. Your Kafeel's instruction for you to leave your accommodation without providing an alternative could be deemed a breach of this regulation.
You can lodge a complaint at the nearest labor office about the refusal of your Kafeel to transfer your sponsorship, alongside his instruction for you to vacate accommodation without providing an alternative.
Remember, under the Ministry of Human Resources & Social Development, you also have the right to seek help through their e-services platform if you face any such issues with respect to legal work conditions including the transfer of sponsorship.