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).
The second is when the corporation is a "listed corporation", i.e. a corporation with outstanding shares listed on the New York Stock Exchange, the NYSE Amex, the Nasdaq Global Market, or the Nasdaq Capital Market. However, the corporation must be a "listed corporation" both at the time of the original issuance of the convertible shares and at the time of the conversion. In such cases, shares may be converted by the corporation ex mero motu provided that the securities received upon conversion are listed or qualified for trading on one of the foregoing markets. Cal. Corp. Code § 301.5(a)(3).
Why does California restrict conversions at the option of the corporation? According to Marsh's California Corporation Law, the drafting committee of the General Corporation Law believed that to allow the corporation this option would create an "irreconcilable conflict of interest":
"If the board were entitled to convert a class of shares into a senior class and was elected by the that class of shares, obviously it might exercise this right only when most advantageous to the shares that elected it. On the other hand, if the board was entitled to convert a class of shares into a junior class and was elected by the junior class of shares, it might exercise this right to the prejudice of the holders of the senior class of shares when it was most disadvantageous to them and for the benefit of the junior class".
§ 7.07 (5th Ed.).
Note to readers: I am a co-author of the the 5th Ed. of Marsh's California Corporation Law.