And that is why the term was used in this context. Because after the Plan is approved, there will be no fractional shareholders. One shareholder will own ALL the newly issued common stock.
Typically when new stock is being issued and old common shares are being wiped out, the terms used are "old" and "new", but that applies when there are multiple entities receiving the new shares. Such as when there are secured bondholders, for instance. But with ARIOQ, it is unusual that the new shares are being issued to only ONE entity, so the use of "old" and "new" is not really applicable. The term "fractional shareholders" is used instead of "old" as there are no fractional shareholders post-reorganization.
It really isn't that confusing, unless for some reason you want it to be.