Is it permissible for an employee, whose employer has failed to provide housing for his family, to rent housing at the employer's expense without his knowledge, given that the nature of the job allows for this?

It is not permissible for an employee to take housing allowance without the employer's knowledge. The employee may terminate the contract due to the employer's failure to fulfill the condition, or remain in the job and demand the housing. If the employer does not comply, the matter should be referred to the competent authorities.