I'm no Derridean, but I've read enough of him and about him to know he was no nihilist. Neither was Nietzsche. But many nihilist have read both and appropriated what they think they've found in their texts for their cause.
Both D. and N. grapple with the problem of truth and interpretation. Both have good enough b.s. detectors to recognize that what most people claim to be truth is some soulless idol that they worship in place of it. What most people call truth has the stink of death about it. Both wanted to find a method of inquiry and way of living that avoided that kind of idolatry, which is the tendency in all human beings when they let their relationship to the Living Real to rigidify. So Nietzsche undertook philosophy with a hammer, and Derrida took Heidegger's idea of 'deconstruction' to perform a similar kind of philosophy whose goal was to free up our relationship to the truth. This was for them a necessary task because In a Positivist age truth had come into the death grip of what McGilchrist calls the hegemony of the values of the usurping Left Brain.
D. and N.'s goal was not to destroy or to debunk for the sake of debunking, but to free the living from its entombment. They take a hammer to walls that imprison truth to liberate it, to make it available again in the lives of those who would love it if they could have any kind of living relationship with it.
There are different interpretations of Derrida's statement that il n'y a pas de hors-texte, which is usually interpreted as 'there is nothing outside of the text'. Derrida was a punster, and I don't want to go down the rabbit hole that follows all the possible allusions. But I think a fair reading of it is that he was emphasizing how every encounter with the truth is one determined by its con-text. I think this is common sense, and it owes a lot to phenomenology, which with people like Husserl, Heidegger, Scheler, Stein sought to liberate philosophy from Positivism. Truth after phenomenology becomes focused on experience rather than on abstractions. And experience and our interpretation of it is always first and foremost contextual.
There is the dictionary definition of a tree, and then there is our experience of a tree, which is different for the botanist or the lumberjack or for a Druid priest in a primeval Irish forest. For each of these the truth of the tree is what shows up for them in their experience of it. The least important thing is its dictionary definition. That tells us nothing vitally important about trees. Phenomenology opens up the possibility to experience the truth of the tree in a living way, it allows us to take seriously what the tree in its inexhaustible meanings might reveal to us. It affirms the importance of the subjective in what a tree actually means.
The tree is in this sense a text, and the text as such is vulnerable to limitless interpretations, and that limitlessness, when taken seriously by anybody who is serious about knowing truth, tells us more about the nature of the truth than any statement about the genus and species of a tree can begin to uncover. To say that nothing exists outside the text is not to relativize what we know but to open up new possibilities for knowing.
This limitlessness is akin to what Buddhism and the apophatic tradition in Christianity affirm about God, which is nothing. There is nothing that can be said that is THE truth about God, and analogously there is nothing that can be said that is THE truth about a tree--or of ourselves or one another. But that does not mean that the effort to say something truthful is futile or that our attempts to say something true have no value.
Because we can never know THE truth does not mean there is no truth. It only means that whatever we can know of it is perspectival, culturally mediated, and always incomplete, and so therefore provisional. That's the human condition, and many sane humans throughout history have been able to live rich, truthful lives within those limitations.
Nevertheless there is always somebody who is tempted to idolatry, someone who wants to put the truth in a straitjacket and keep it locked up in the attic. They are usually the kind of people whose obsessive need for control leads them into positions of power in a society's political and religious institutions. They're the ones who freak out when someone challenges their rigid ideas about what is true or not. They're the ones who close themselves off from the truth because it scares them.
Language makes the uncommon common, Nietzsche says somewhere. Yes, mostly that's true, but not always. And in that statement, he affirms the possibility of experiencing the "uncommon". Cliches once weren't stale even if whatever vitality was first in them is doomed to become stale over time. Religious language is like that, too. But there is always in any text the possibility to take a hammer to it, to crack open what entombs it, and to discover the living thing in it to which such texts first gave utterance. But the utterance isn't the truth; it's just a provisional attempt to articulate some experience of the Living Real that is always inadequate to whatever the experience of it might have been.
And for this reason language--and other symbolic forms--can work as a portal to the uncommon. It is not what is actually literally said in the symbolic forms, but rather what we come to see through them into something uncommonly bigger and more vital. Some statements are more adequate than others because they articulate more effectively something uncommon in a way that has the fresh smell of truth about it.That's why we still read--or should--Homer and the Bible and Plato and Shakespeare. Because the language we find there has this enormous potential to surprise us. We think we know already what we will find in these texts, but if we have an openness to them, we will be refreshed by something unexpected, something living. We have to cultivate a mood that Heidegger called, following Meister Eckhart, gelassenheit, which is similar to Keat's negative capability. Look it up.
This approach leads often to an awakening of something dormant, to a memory of something forgotten. Heidegger says we moderns suffer from a forgetfulness of Being, and one way to remember what has been forgotten is to spend time with important texts. The disclosures that come if one makes the effort have the freshness of life about them, and we are refreshed by it. That is the kind of truth that is worth knowing about. It is not THE truth, but it points to it as an inexhaustible spring of vitality.
This kind of remembering is something no AI will ever be able to do because machine memory cannot forget. It's the forgetting and then the remembering that is the peculiar human thing. And for that reason human memory is capable of resurrecting the dead.
And so, while it might be that the symbolic forms that once articulated something living no longer live for us, it does not mean that what once lived is now dead. It's just gone underground. It can be remembered, resurrected. Those forms once steeped in uncommonness have become stale and common because of the human proclivity to be distracted by other shiny objects--in our case the produce of techno-capitalism. Nevertheless we still live in a society shaped by symbolic forms that retain their potency even if it is not something we have easy access to. A tradition dies because people let something die within themselves, and this is how I take what Nietzsche means when he says that God is dead. It is not really God who is dead, but we who are.
And this is the value of Derrida's deconstruction--to break open the sarcophagi in which these once living texts lie because nobody who plays a significant role in shaping the culture reads them anymore--texts like those of Plato and Augustine, for instance, that D spends a good chunk of time with--and to find again what's living in them, and to critique what is not. What's important is not what Derrida finds there, although you might be surprised to learn what he does find. Rather what's important is to follow his method, to interrogate the great texts, and like Jacob wrestling with the angel to derive therefrom a blessing.
See also "Deconstructing God".