Paid Partial Rent - Can they evict?

I’m in California. I paid part of the rent, but told them I wouldn’t be able to pay the rest on the date we verbally agreed upon (12/20). They said they would still put up a for rent sign, even though I made it clear we arent leaving until we have to even if they start the eviction process because we have nowhere to go.

They can’t start eviction process since they accepted partial rent, right? And if I come up with the rest by the 31st plus the whole rent by the 5th (the due date), they can’t evict us based on no payment, right???