The duration of copyright depends upon the jurisdiction in which the work is published.
In the EU (and UK) this is 70 years after the death of the author (if there are multiple authors, it is 70 years following the death of the last surviving author).
In the USA there is a “cliff” currently at 1926 I believe, that moves forward each year – effectively works prior to 1978 are protected for 95 years. Works from 1978 are protected for 70 years after the death of the author. There is a special rule for works where the “author” is a corporation, whereby works are protected for 95 years from the date of publication.
This is a general outline, and there will be specific examples where this does not apply: “Peter Pan” is protected by a perpetual copyright in the UK, works in the USA where the option to renew was not taken up will have copyright expire, even where created after 1926, 28 years from publication (an example of this is the film “It’s a wonderful life”).
So, in general, works where copyright has expired are open to adaptation/republication without permission of authors/rights holders.
Where one should be careful about this, in a moral sense, is where your adaptation might mislead the public about the original work. During the 19th century foreign works were not protected in the USA, and it was common for those works – particularly British works – to be republished in the USA, that is, not authorised by the rights holder. Some problems that arose from this practice was that sometimes parts (even whole chapters) were not included in the editions published in the USA, and sometimes completely different works were given the title of a foreign work. In both cases this would have the effect of deceiving the public about essential qualities of the work.
In modern times there are many examples of classic works that have been abbreviated or otherwise subject to adaptation – the fact of this alteration is not always obvious to the reader or potential purchaser.
So, in order to prevent confusion, it is probably good practice to ensure that your adaptation is distinguishable from the original. For example, the title might make it clear that it is an abbreviated or adapted version of the original.
It is worth noting that your proposed adaptation would have its own copyright protection (for whatever term is appropriate in the jurisdiction where it is published). This should give you additional reason to be cautious.
You should therefore beware of basing your adaptation upon someone else’s adaptation, since you may infringe the rights of that adaptation. This is probably a rare case, but may be present in works that were left unfinished by the original author (where another completed the work, at a date that may be subject to copyright protection), or were otherwise changed or adapted after initial substantiation.
Particular care should be excercised in the case of translations, where even ancient works may have modern translations that are subject to copyright (for example, both Seamus Heaney and Ted Hughes completed many translations/adaptations of ancient and foreign works into modern English, and those will have copyright protection until 2083 or 2068 respectively - or perhaps later if the term is extended).