Can S Corporations issue convertible notes/debt?

I was reading this answer and am a little confused - how is convertible debt precluded by being an S corp? (rather than C corp)

Is this just an overstatement? I understand that one typically would have a C corp for transactions that involve convertible debt - for classifying different shareholders. But is there really some fundamental reason/prohibition on convertible debt in an S corp?

I must be missing something.

It's because a convertible turns into pref shares, or at least some pref shares, at the company's next financing event, usually a Series A round. As soon as those pref shares come into existence, S-Corp status is gone. It is theoretically possible to have a convertible that converts to common stock, but that means the valuation event that triggers the conversion can't create a new share class, which is rare. Nonetheless, you're free to be an S-Corp and do a convertible (the new share class won't come into existence because of the convertible). Just know that you'll probably change to a C-Corp at your next round, which isn't usually a big deal. The change to C-Corp (either from LLC or S-Corp) is actually really common at a Series A round (though it's easier to go from S to C than from LLC to C).

There is also the issue of number of shareholders. Don't forget that sub-S corps can only have up to 100 shareholders, so if you issue convertible notes, and the option to convert to shares of common stock is exercised, the holders of those notes might push you over the 100 shareholder limit.

Interesting if the notes become publicly traded as some kind of asset backed security...then if it got chopped up into some kind of financial vehicle, you could end up with millions of people "owning" a tiny percentage of the right to buy a share. There are probably terms in the convertible not (i.e., you must own a full right to acquire a share, etc.) but I don't know what the feds would think about that.