Cluedrew has already added an exceptional flavour review above, so I wanted to provide a more logistical overview of what this card does and when to use it.
If you're unfamiliar, Netrunner is an expandable card game with a continuously updated ban list and regular set rotations. This does a lot of important things regarding balance, staleness, creative opportunities and accessibility but one of the smaller things it does is open up opportunities for what are commonly referred to as "near-prints." Cards that closely resemble prior cards that have been banned or rotated but with some critical details changed. This allows one to attempt to keep the best and most interesting parts of a card's identity while trying to fix its most problematic elements.
So notable examples include cards like Spin Doctor which closely resembles Jackson Howard but has a limited use card draw effect, recurs 2 instead of 3 cards and costs 2 instead of 3 to trash, limiting its strength and making it cheaper for the runner to trash it. Or Diversion of Funds which closely resembles Account Siphon with the additional cost of a click and a credit to play as well as reducing the amount gained so that it represents a 10 credit swing instead of 15 should it succeed (though it no longer gives the runner tags either).
Ashen Epilogue is a "near-print" of Levy AR Lab Access, a potent card that allowed you to recur the entirety of your heap back into your stack, essentially refreshing you back to the game start (while allowing you to keep all your installed cards, credits and agenda points of course). Since cards almost invariably get trashed, be that simply from playing events or from using trashable resourses, hardware or programs cards will end up in the heap. And, since those cards have value and uses, it can be important to get them all back.
And that's saying nothing about rigshooting or Net Damage, Meat Damage or Core Damage removing key cards either.
In a more abstract sense, if you were worried about running out of cards, you could simply make a larger deck, including more cards to last you longer in a more protracted game, however, due to most cards being limited to a playset of 3, this runs you into the problems of consistency and efficiency as you are forced to gradually bloat your deck with unnecessary and inferior cards to avoid running out of them. Levy Ar Access solved that problem by letting you make a tight, efficient deck with all the best cards and then just recurring them once you've gone through your whole deck. Giving you most of the potential upsides of a much larger deck, without any of the drawbacks.
Ashen Epilogue tries to preserve the potential of such a card while limiting its universal safety with one major change "remove the top 5 cards of your stack from the game." Put simply, if your goal was to try and use Ashen Epilogue as a safety blanket against key icebreakers or combo pieces getting trashed then you run the even bigger risk of accidentally removing those cards from the game, putting them even further out of reach.
A smaller change from Levy to Ashen is that Ashen is a 2 influence neutral while Levy was a 3 influence Shaper card, this change makes the card slightly more accessible for non-Shaper factions and slightly less accessible for Shapers.
When to Use
This card is ideal if your economy is particularly dependent on finite cards, event-heavy econ like Sure Gamble, Creative Commission, Dirty Laundry, or Bravado all come to mind. As well as decks that trash their own cards for money through Aesop’s Pawnshop, Spec Work or Isolation. But is markedly less useful in decks with self-sustainable econ like drip or the old Magnum Opus.
It's particularly valuable in Anarch decks where self-trashing is common Steelskin Scarring, Strike Fund, Moshing, The Price, Eye for an Eye, Audrey v2, Lago Paranoá Shelter, Friend of a Friend and many many more. It's practically a must-include for Esâ Afontov: Eco-Insurrectionist where without it she would probably mill herself out long before she mills the corp.
It also has applications in run-event heavy Criminal decks, the aforementioned Bravado, Dirty Laundry and Carpe Diem all being core to high-tempo Criminal econ. Or even in a high card draw Shaper deck where you'll regularly see Dr. Nuka Vrolyck, Diesel, Aniccam and Lat get through the entirety of your deck before the end of the game.
In terms of timing, this card is best used when your deck is empty to maximise the potential number of cards recurred, but it's also best used on an empty hand if possible. Remember, spending 5 credits just to draw 5 cards is good value even if the massive recursion effect wasn't even there.
When Not to Use
As mentioned previously, if you need to recur specific, highly-valuable cards more safely and reliably, there are other better options, Harmony AR Therapy is one of the most common at the time of writing alongside Simulchip in Shaper while Anarchs have Labor Rights and Privileged Access, all of which are quite good. There are also Katorga Breakout, Rip Deal and Test Run though they see relatively little play comparative. All of these cards can more precisely and reliably recur a single card you need, allowing you to recover that one lost breaker or combo piece without risking it being removed from the game and without having to recur everything else in your Heap at the same time and sort through your deck all over again.
Edit: Something I forgot to add is that you should almost always run this as a 1 of. Since the ideal time to use this card is once you've gone through your entire deck, you're guaranteed to draw it by the time you want to use it and you almost never need to cycle through your entire deck 3 times over. Thus including multiple copies brings nothing but drawbacks, namely, that you double the odds of drawing it early in the game when it's a dead draw that will clog your hand, as well as the extra two influence cost.
TLDR: A "near-print" of Levy AR Lab Access that allows you to recur almost all cards from your Heap back into your Stack, best used in self-trashing Anarch decks but not particularly safe or reliable for recurring any specific card in your Heap.
