I have been a caregiver for an elder of the puyallup tribe I was hired as a w9 employee that mean it pay may own taxs at the end of the year. Do to cuts I was let go, so my question is can I get unemployment

No. As a self employed individual you can't get unemployment.

No, you can not collect unemployments
You were not "let go" or "laid off" your contract for your services was cancelled.

You "owned" your own buisiness as a self employed person, Thus the reason you pay needed to be higher than normal pay check, to cover your business costs.