It depends.
Your first choice should be to use your employer-paid time off.
If you cannot go to work because you don’t have childcare while schools are closed, you should call your employer and let them know why you are absent. If your employer fires you or lays you off while you are absent, then you may qualify for unemployment.
However, you are required to be able and actively seeking work each week you collect unemployment benefits. If you don’t have childcare and can return to your job or accept a work offer, you will not be eligible for unemployment benefits. If your situation changes, you should contact the Washington State Employment Security Department.