You can file a new case, but it will not be heard.

If so it doesn't have a filing requirement. 

I am in between tenants and am even considering leaving the house vacant.To collect overdue rent, I believe in normal times you would serve them the appropriate form, and then file for eviction after 14 days.

HOWEVERThey did not change or extend the deadline to FILE.

Apologies for posting so generally, I have been trying to search the BP file place, but the search appears to be not working or working poorly. 

Perhaps you want to file eviction on any tenants who do not pay by the 10th, but larger companies may have policies in place to not file until the 15th and cannot accommodate your needs.  

You can also look online in many places to see court records and see if he filed other suits or if other people filed suits against this current landlord.

I would remind them that an eviction and/or collection filing won't serve them well in the future nor give you any satisfaction so it's in everyone's best interest to "move on..."

Here's the official COVID-19 website for California that the state just launched: https://covid19.ca.gov/.It has current information on how to stay healthy and avoiding catching/spreading the virus, links to school districts (so parents can find out which schools are closed) & public health authorities, as well as helpful resources that people will likely need during this time of crisis, such as how/where to file for unemployment, disability, family leave, or get help for small businesses. 

While evictions are currently halted nothing prevents a landlord from filing an eviction action with the court.