Scenario:

Part-time exempt in California
Work week: 20 hours a week; 4 hours per day, M-F
Salary is $455 per week
No sick time policy
No available vacation time

If the employee call in sick 4 days out of 5, do the employee still get paid $455.00 for that work week? Please explain.

As far as I know you don't, especially if you don't have a sick leave policy and you aren't full time. Sick time will be deducted from your check and you will get paid for the hours you worked.