This is actually a recent development. If I may expand upon this a wee bit.
The term Sui Iuris" refers to a law of their own. In other words, governed and administered according to a set of rules which are different from the Latin. This became possible when the CCEO was created (1990), except that it lumps all of the more than twenty different Particular Churches into a “one size fits all” set of rules that is full of a lot of compromises to smooth out the differences between them.
Before this, they were all just particular Churches with different rites, and subject to the Latin Code (1917, 1983). Any diocese can be considered a Particular church and potentially have a set of ritual practices identifiably their own, thus the diocese of Krakow might be practicing one rite, the diocese of Milan another and the diocese Cluj another. They were all considered part of the “One Church”, with particular referring to a “part of the whole”.
Now these various eastern church bodies are deemed “Autonomous Particular Sui Iuris churches”. Which means (in a sense) that they…[LIST=1]
*]have a name of their own (not self headed, but self-named),
*]are a part of the whole,
*]have a law of their own.[/LIST]They do not have the right of self determination. Although for some of them it was this right which (in theory, voluntarily) brought them under the control of Rome, they do not retain that right to decide to place themselves under another church authority.
The term “Orthodox in Communion with Rome” is bandied about quite a bit among Eastern Catholics. I used it for a while myself once. The plain fact is there are very few Eastern Catholics who would be considered truly Orthodox by the Orthodox churches, they would have to believe everything Orthodox teach, and reject everything Orthodox reject.
That is problematic, if applied in this case to someone under theoretical obedience to the Supreme Pontiff that would make them appear to be Cafeteria Catholics at best. If the definite denial of certain Latin dogmatic constructions (Purgatory, Filioque, Papal Universal Jurisdiction, etc…) is tantamount to heresy then such people could possibly be suspect of that as well.
However, there is a provision in the Catholic church to allow Orthodox (as well as PNCC, and probably Church of the East) to receive communion in the Catholic church, provided they have the necessary permission from their own (Orthodox) bishop.
If that were to somehow actually happen, one would see an Orthodox Christian “in communion with Rome”, without actually being “under” Rome. I don’t think that either the Orthodox Churches, nor the Vatican can currently admit to such possibility. It is highly theoretical, such permission is not routinely given or sought from Orthodox bishops.
The Orthodox normally stake out the position that if one accepts communion from a Catholic priest, one is assenting to what that church teaches and is no longer Orthodox. Thus “Orthodox in Communion with Rome” is something of a chimera.
Interesting possibility to muse over, but more of a fantasy than anything else.