Longer answer: The virtue failed apprentice does not affect xp at character creation so the easy solution is to do nothing special and proceed with normal companion/grog character creation and voila no problem created where non existed before.
you should keep in mind that the virtue does not specify where in apprenticeship the failure happened, and it is equally possible to assume that the apprentice had their Gift broken at the opening of the arts as it is at the 14th year of apprenticeship. AFAIK there is not official ruling on when it is most likely to happen but IMO the opening of the arts is the best guess at where most apprentices fail since it is the only time in apprenticeship where the master must directly interact with the apprentices Gift.
a normal apprentice accrues 240 xp and 120 levels of spells in 15 years, equivalent at character creation to 360 xp if you are a magus or 24 xp/year. of course you could argue that the spells are lost which puts us down to 240 xp or 16 xp/ year. if you then proceed to argue that the arts are also lost that puts you in the situation of having to figure out how much xp the apprentice put in arts. This you can only solve in 2 ways: 1: make an assumption or 2: by using extremely detailed play and create your failed apprentice character on a year by year basis and figure out exactly how much they lost that way.
If you go with option 1 I would say that a 50:50 distribution of abilities to arts is reasonable at gauntlet with an early focus on abilities and a late focus on arts, meaning that the earlier the apprentice loses his/her Gift the better it is for them. A 50:50 distribution at gauntlet is IMO consistent with the magi I have seen in the core book and in play, but I have not made any effort to prove it beyond a little analysis a long time ago when I made a character based on the templates in the core book so I may well be wrong.
for extremely detailed play I would offer the objection, that even though you are in principle doing the very best you could, but you are still making a character knowing that all xp put into arts and spell levels will be wasted which is likely to skew your effort even if you dont notice it.
I would say it depends when the apprentice failed. Quite simply the first thing that the parens would do is teach them latin, magic theory and liberal arts, just to fill the requirements and so that they can help out in the lab. Then give them the other skills they might need (lores, crafts etc based on houses) and then spend more or less the second half of the apprenticeship teaching the arts and spells.
I would find it fair that the apprentice has no arts or very low arts. Although have an art at 5 and some teaching would make the failed apprentice very handy and possibly could make a decent living teaching young magi...
A Failed Apprentice has access to Academic and Arcane Abilities, but I'm not sure I understand the bit about "if the Gift was not completely destroyed, you may have some Supernatural Abilities"...normally these are accesible if you just take the relevant Virtue, I assume this is still the case, and the 'destriyed Gift' if just the explanation as to why there is still some remnant of a mystical skill.
Anyhoo, since Arts are no longer useful, I'd just ignore them. Unless the concept is that the Gift at some point will be restored. In that case, do keep track of it.
Otherwise it doesn't matter to me when the apprentice lost the Gift, or how much Hermetic training they had. I'd make it a Grog, if the Gift was lost early into apprenticeship, or a Companion if lost later, but it really mtters most how important this character is intended to be.
I would say yes. They might not be able to put them in practice, but they could still teach or write about them. If they have good Comm, cranking out 2 or 3 tractatii on arts could see them financially set for life.
I thought it had to do with the idea that every Gifted person automatically has a free Supernatural skill/virtue, because of the Gift. Is this free Virtue a side-effect of the Gift (in which case it may remain once the Gift goes), or is the Gift a pre-requisite of the virtue (so the virtue won't work without the Gift)? I don't recall the 5th Ed book taking a definitive stance.
Then there is the bit in, Hedge Magic I think, where learning individual supernatural Virtues has less synergistic power than learning the same supernatural Virtues as part of a Magic Tradition - available only to the Gifted.
I would expect most parens to focus on academics first- especially Latin, Artes Liberales, and Magic Theory- it is the third after all which makes an apprentice useful and the first two which allow an apprentice to read in the seasons when the magus has no other use for them. Thus a failed apprentices losses are reduced by the tendancy to front load the abilities they will retain. On the other hand I would expect the apprentice to be trying to learn the arts and spells more quickly, since those actually do something.
If you want to get really detailed it will also depend on house- a verditius might have focused a lot of effort into teaching a craft ability, A merinita faerie lore, a Jerbiton social abilities unrelated to magic...
Probably no, if the failure comes from destruction/suppression of the Gift, even partial. Check out the Hermetic/Story Flaw Suppressed Gift [Apprentices p.13]:
"...While the Gift is suppressed, the character cannot perform Hermetic magic, improve his Arts, or perform the Parma Magica... Such a character may still use Supernatural Virtues and Abilities."
In general, there are many ways an apprentice can fail.
He can fail because he loses the Gift. He can fail because he had no Gift to start with, and this was realized at some point, possibly very early or even at Gauntlet time. He can fail because he never manages to get to or complete his Gauntlet, while keeping all his Arts and Gift intact (very rare, but not inconceivable; check out the Fenistal in GotF, p.114).
One thing to keep in mind is that Failed Apprentice is a Social Status Virtue. As such, its main purpose is to provide ... a social status. It also provides access to some classes of mundane abilities (and a controversial ability to "help in the lab"), but that's really a side effect. Basically, it says "you were meant to be a mage, but you did not make it".
To describe what other abilities/powers are available to a Failed Apprentice, you should choose what type of character he is (Grog, Companion, Gifted companion, Mythic companion, Magus), and combine that with appropriate Virtues. For example:
a) An apprentice whose Gift was completely destroyed when it was opened ... make him a Grog or Companion, with no supernatural Virtues whatsoever. He might know some Latin, perhaps a little Magic Theory, and a few Arcane abilities by exposure. Total xp as per standard Grog or Companion.
b) An apprentice whose Gift proved unopenable by Hermetic Magic, despite an ambitious Bonisagus master trying very hard. Make him a Companion, possibly with the Gift and either a Curse (will never become a Hermetic mage) or a whole lot of Supernatural Abilities, perhaps from some Hedge Tradition. A Mythic Companion can work too. Or give him the Flaw Magical Air instead of the Gift, to represent the fact that his Gift is just plain "inaccessible" to any form of magical training, at least until he undergoes some mystic ordeal. Total xp as standard Companion or Mythic Companion.
c) An apprentice without any Gift to begin with who somehow bluffed his way all the way through apprenticeship (Larta style), but was found out at his Gauntlet. Companion, or perhaps Mythic Companion (say, a Devil Child). Again, total xp as standard Companion or Mythic Companion.
d) An apprentice who had the false Gift, and lost it alongside with all his Arts thanks to a miracle. Companion, or perhaps even grog, with the standard 15xp/year to represent what "useful" abilities he's left after losing the Gift; this is probably the result of excellent tutoring by demons. You can always reduce those xp with an appropriate Flaw.
e) An apprentice who died in some lab accident and came back as a ghost or faerie. Or perhaps just went through a "gauntlet" that transformed him into a living god (Transformed Human, Faerie etc.), it's fundamentally the same Grog (e.g. magical ghost), Companion or Mythic Companion, with xp determined by character type (magical characters by Season, faerie ones by the age of other PCs etc.).
f) An apprentice whose Gift was suppressed at some time during his apprenticeship. Build him as a magus or an apprentice (from Apprentices) and give him the Suppressed Gift Hermetic Flaw.