Tesla is keeping its Fremont, California car plant running during "shelter in place" orders initiated across counties in the San Francisco Bay Area to curb the COVID-19 coronavirus outbreak, including Alameda County where the factory is based.

Employees at Tesla received emails about working during the pandemic and shelter-in-place orders late Monday, including one from CEO Elon Musk, and another from former compliance attorney at Tesla, Valerie Workman, now head of HR for North America. CNBC has seen copies of both emails.

In the "everybody" e-mail about remaining despite the efforts to contain COVID-19, Musk wrote:

"I'd like to be super clear that if you feel the slightest bit ill or even uncomfortable, please do not feel obligated to come to work. I will personally be at work, but that's just me. Totally OK if you want to stay home for any reason."

Musk assured employees in the email that, as far as he knew, no Tesla worker had been confirmed as infected with COVID-19 as of March 16.

Bloomberg and the Los Angeles Times previously reported on the factory's status and the e-mails.

Tesla recently began deliveries of its new, crossover SUV, the Model Y and is under pressure to get as many of these made and delivered to customers as possible before the end of the first quarter. Tesla has yet to revise or withdraw guidance for 2020 or the first quarter of the year, even though analysts expect the pandemic to cause a 20% drop in car sales in the US this year.

Two employees and the family member of one Tesla employee told CNBC on Tuesday that workers there feared taking time off would impact their performance reviews and lead to their being fired later. And many cannot afford to go without income for the three weeks of shelter-in-place orders.

One employee said that many Tesla colleagues had decided to take voluntary, unpaid leave and those who were left to work at the factory were now doing the jobs of two or three people at once. These people asked to remain unnamed because they were not authorized to speak with the press.

Alameda County's public health department reported 27 confirmed COVID-19 cases as of March 17, 2020, but did not specify if any had occurred in Fremont or near Tesla's plant.

Tesla did not immediately respond to a request for comment.