Kind of yes kind of no, depends where you live and what “moratorium” means. The state website is actually not too bad at explaining what is going on …. https://housing.ca.gov/. A lot of the tenant organizations also have some information but the sites I found seems to be a bit out of date.
In California in February the governor signed a law extending the moratorium on evictions to June 30, 2021. It isn’t really a full moratorium but is stronger than the last round. Tenants are still responsible for paying what they can and for unpaid amounts to property owners, but those unpaid amounts cannot be the basis for an eviction, even after the moratorium ends. And SB 91 prohibits the selling or assigning of rental debt that was accrued from March 1, 2020 through June 30, 2021 until the end of the moratorium for some tenants and the prohibition is permanent with respect to the rental debt of people at or below 80 percent of Area Median Income who meet the eligibility requirements of the Rental Assistance Program. This is actually a very important provision because it means the landlords can’t sell the debt to other companies that would try to collect it as “debt” instead of back rent which is protected. Landlords can’t charge late or collection fees. Also even after June 30, 2021, no tenant can be evicted, if they pay 25% of the rent owed from September 2020 through June 30, 2021, either monthly or in a lump sum before the final day it is due and attest they face a financial hardship due to the pandemic. This is complicated and hard for a lot of tenants to follow and means that some will be evicted despite protections—trying to get relief in court is expensive and time consuming and may not happen.
In addition, California landlords might be able to get repaid for past due rents from federal funds the state will receive if they are willing to take 80% of the rent. If a landlord refuses to take the 80% (forgive 20%), then tenants may be able to recoup up to 25% of the past due rents from the fund. Then, if there is any money left in the fund, it is possible some future rent could be covered, then utilities and household expenses in that order. It’s confusing.
Landlords can still evict tenants for “just cause” in California despite the moratoriums. Those “just cause” factors include nonpayment of rent (for other non-Covid related reasons), conducting criminal activity on the premises, or destruction of the property, etc.
Some cities have additional protections—San Francisco and Los Angeles do and they provide a bit broader protection but still require certification as required by the state that the non-payment is related to Covid-19 or the Federal CDC Order which appears to protect tenants from eviction during this time even if the inability to pay rent is not directly related to COVID-19 in order to prevent the spread of Covid. https://www.cdc.gov/coronavirus/2019-ncov/covid-eviction-declaration.html It is not clear what legal force this order has unless it is incorporated into local or state rules as Los Angeles did.
The upshot is that tenants in California have some protections if they cannot pay rent due to Covid-19 related income declines, but it is no full “moratorium” on evictions.
Despite the legal moratorium, some landlords are still giving tenants eviction notices accompanied by threats of collection or court notices. Also, some landlords have cut off utilities or failed to make necessary repairs in order to force tenants out. Though some or all of this may be illegal, but some people will move, rather than fight what appears to be a losing battle.