It is nearly impossible to imagine Tesla Inc. without Elon Musk — its chairman, CEO, largest shareholder and public face.

But the Securities and Exchange Commission's lawsuit Thursday has raised questions about the executive's future at the electric car company, sending shares spiraling. The agency accuses Musk of misleading investors with his infamous Aug. 7 tweet about taking Tesla private and seeks to ban him from serving as a director or officer.

That possibility, however remote, cast a pall on the final days of a rocky quarter and is likely to renew concerns about Tesla's lack of an operating chief or a clear No. 2. This weekend was supposed to be a celebratory milestone, with thousands of Model 3 sedans finally making their way to customers at delivery centers across the U.S. as the company made a final push to achieve sustainable profits. But once again, a drama surrounding Musk is taking center stage.