Is an employer responsible for paying employee for the days they are unable to work?
An employer is not responsible for paying employees for time off work due to an on-the-job injury. All employers are required to have workers' compensation insurance, however, and so the employer's carrier will pay the injured worker if he/she misses more than 7 days of work.
Some employers choose to voluntarily allow their injured employees to use sick/vacation/PTO hours to make up for the difference between their regular pay and what workers' compensation pays (which is always at most 2/3 of their regular gross wages.) I've always considered that to be a win-win policy, because the employee doesn't fall behind financially, and it doesn't really cost the employer anything.