May a California corporation issue shares that are convertible
ex
proprio motu into shares of any other class or series or any other of its securities? The answer is "yes" but only if that right is provided in the articles of incorporation and then only in two limited circumstances.
The first is when the corporation has a license or franchise from a governmental agency to conduct its business or the corporation is a member of a national securities exchange registered under the Securities Exchange Act of 1934, provided the license, franchise or membership is conditioned upon some or all of the holders of its shares possessing prescribed qualifications. In such cases, the the shares may be converted at the option of the corporation to the extent necessary to prevent the loss of that license, franchise or membership (or to reinstate it). Cal. Corp. Code § 403(a)(2).