We will be watching this forum throughout Coronavirus/Covid emergencies to post information and to answer your questions about affected US immigration and visas:
Please, could you help me with this?
I've had O1 visa for 5 years. What happens if a quit my job? Do I loose my rights to stay in USA. Can I stay here searching for another job?
If you are sponsored by an agent representing you and your employers (such as Mastery Productions LLC) you will be able to work with anyone in your field, and it's not a problem if your work stops and you are searching for another. You are not dependent in an employer in order for your visa to be valid. This is why most O1 artists or scientists prefer such sponsorship.