I'm afraid the phrase in question lacks the article. The correct phrase is: Ejecutoriado que sea el fallo, ...
Notice that google searches (Searches) show more than 2,600 results for the phrase with "el", and only one without it: your question at this site.
Judgments (or decrees) are of course executed (signed) by the judge and, as a result, enforced, that is, put into practice. "ejecutoriado" is closer to this idea of "enforcement". (Supporting source)
To translate something legal in the subjunctive passive form (it can be regarded as imperative, or as the subordinate clause of "Ordeno que se confiera"), two formulas can be used:
- May X be + past participle ...
- Be X + past participle ...
A good translation is not one that makes the text understandable for the layperson. A good translation is one that imitates the original to the extent that nothing is lost -- not only the content of the original, but also its style. A good literary translation needs to sound literary, a good technical translation needs to sound technical, and a good legal translation needs to sound legal, not like everyday speech.
"subinscripto" does refer to "fallo" (masculine). The point is that the primary record of the judgment will remain in court, while a copy is being requested for the judgment to be also entered in the Civil Register (the book) or filed with the Civil Registry (the office). What I mean to make clear at this point is that "registro" is ambiguous in Spanish. This second entry or recording counts as a secondary filing (subinscripción).
A possible translation could be:
- Once the judgment has been enforced, may a certified copy thereof (be made to) be filed with the Civil Registry / recorded/entered in the Civil Register. (I think "be made of" can be omitted, as it is implicit that a copy will need to be made to be able to proceed with its filing.)
Sorry I can't help with the etymology of "fallar" and "fallo". In English, we can say that a judge or court pronounces/renders/passes/issues a judgment (emite/pronuncia/dicta una sentencia/un fallo or just falla).