A question I did not answer at the time, regarding this:
One wonders, when she was revived, did she reinherit back any of her titles or property?
Titles are the easiest one to answer, *there*, and the short answer is “some of them, according to their nature”.
To answer in a rather longer manner: if we for the moment discount titles of privilege (i.e., those titles which exist simply to be purchased by/to recognize the contribution of personal resources to the public good) and assume that private titles more or less follow the same rules as public ones (an essentially accurate assumption), it looks something like this:
In Imperial praxis, as defined by the Imperial Charter, there are three classes of titles: runér, praetorate, and exultant. The former two are both functional – by definition, the holder of a runér title has the Imperial Mandate over some demesne somewhere, physical, virtual, or abstract, and explicitly executes all the duties attached thereto. Likewise, a praetor holds some office somewhere in the Imperial Service, and the title comes with the job, to provide the precedence and dignities appropriate to the job.
Exultant titles, contrariwise, are not-implying-you’re-done-but-still-post hoc rewards for merit, accomplishment, and excellence, and as such are not explicitly tied to executing any particular duties except for the rather generalized one of continuing to be the awesome soph you were formally recognized as being.
So, the rules for these were set a long time before it ever came up in this particular case. Exultant titles, you keep and can reclaim; they have no dependencies on anything unless you go so far outside the pale that the people authorized to initiate such a case can persuade the Curia to impeach you. Runér and praetorate titles, on the other hand, are strongly linked to doing the job, and as such the condition there is and has always been incapacity. Suffering from “not-dead-in-the-most-technical-sense, long-term, whole-body frostbite” adequately qualifies as incapacity, so those titles do pass – but, then, unlike most Earth cases, they would also pass if you were merely comatose, or suffering from other lengthy medical conditions that meant that you couldn’t perform the duties of the office, because none of those titles are ornamental and someone’s got to.
You do, however, automatically receive the corresponding courtesy exultant title for ex-runér/ex-praetors, because that’s part of normal succession procedure. Which is to say you keep the honors of the position, after all, you earned them; it’s just that you aren’t the person people should be taking their petitions and paperwork to any more.
(As for the possibility of reclaiming those titles: in most cases, that wouldn’t be automatic, although your successor may choose to hand it right back to you. There are a few exceptions due to their own special rules: most House charters reserve the position of “genarch”, for example, to the oldest living family member with descendants, and if the person fitting that description happens to do so because they just came back from the dead, well – ain’t no rule against that, and they’re still the oldest living family member with descendants, so.)
Property-wise: That’s somewhat more complicated, and I don’t want to go into too much detail because that time period is exactly the time at which the legal rules on that sort of thing were in flux, and I have not yet nailed down the exact dates of what fluxed when.
In the modern era, of course, it’s not even a question. You aten’t dead until there’s no information-theoretically recoverable mind-state recognizable as you available anywhere, or alternatively, have personally merged with the Transcendent god-mind, so no-one’d even think about running probate just because you happen to be chillin’ right now.
Back in the day, of course, this was more complicated when you could be dead without being dead-dead, but Imperial law has always been much more generous than ours when it comes to ensuring that the dead can still get their will done, not like mere animacy should be able to impair the sacred obligation of contracts, after all. So it would not be at all hard for her, or anyone else trying this, to set up the appropriate instruments to hold her stuff in trust and then give it back to herself. (That would be necessary because it’s not like they could unprobate, as that would inevitably be ex post facto.)
(And she probably didn’t do that for all of it, either – this being, after all, still very experimental. And, well, one can always get more money.)