Can I quit my job due to unbearable conditions and still receive unemployment compensation?

The employer is on notice that you have a shoulder injury and it should be taking the issue seriously. The injury may be work-related. If it is, you should have promptly reported the injury and filed a workers' compensation claim, and should be giving the claim details to the doctors' offices so they can bill the workers' compensation carrier. If the injury is not work related it still may be disabling and you may qualify for protection under the California Fair Employment and Housing Act if your employer employs five or more employees. The employer should be engaging in the interactive process to discuss reasonable accommodations if you have a physical disability. The cut in hours could be considered disability discrimination and adverse job action. However, the employer might say it is accommodating your restrictions. The employer should consider other types of work and schedules with you.