I'm sub-renting a house in CA (from someone renting to the owner).
That person has no home insurance.
I want insurance:
Can I take a renters insurance?
Is it the original renters role to contact it?

Thanks!
My question is:
as a sub-renter (we have a written contract though), am I legally entitled to contract the renters insurance for that place?

you should always insure your personal property!

Yes, you NEED to have renters insurance to cover YOUR stuff, and YOUR liability if YOU get sued related to this premises.

You always have to insure your own stuff.