When the injury causes death of an employee who leaves no dependents, then the employer shall pay the reasonable expense of the employee’s sickness, if any, and the expense of burial, as provided in sections 85.27 and 85.28, and this shall be the only compensation; provided that if, from the date of the injury until the date of the death, any weekly compensation shall have become due and unpaid up to the time of the death, the same shall be payable to the estate of the deceased employee.