The Derrida of the 1980s and 90s surprised many of his critics and some of his admirers by turning, with increasing directness, to questions of politics, ethics, law, and religion. This was not a conversion or an abandonment of deconstruction. It was an extension: the same structures that appear in the analysis of language and textuality reappear, transformed, in the analysis of justice, hospitality, democracy, and the gift.
The key move in the political Derrida is the concept of the undecidable. Genuine ethical and political decisions, as distinct from the mechanical application of rules, require passing through an undecidable: a moment in which no algorithm, no rule, no general principle can determine the right answer, and a responsible subject must decide anyway. If you could simply apply a rule, there would be no decision, just calculation. Decision, in the fullest sense, requires the suspension of the rule, the encounter with the irreducible particularity of the situation, and the taking of responsibility that cannot be fully justified by appeal to any pre-existing framework.
In "Force of Law" (1989), Derrida distinguishes law (the calculable, enforceable, positive legal system) from justice (the incalculable, infinitely demanding, impossible-to-fully-achieve demand that every singular person be treated in their singular particularity). Justice, he argues, is always yet to come (à venir), it is not a state that can be achieved and then maintained, but an infinite demand that every existing legal and political arrangement always fails to fully meet. Deconstructing law is possible and necessary: laws can be shown to be historically contingent, ideologically constructed, internally contradictory. Justice itself cannot be deconstructed, because it is not a present system but an infinite demand that grounds the very possibility of critique.
In "On Cosmopolitanism and Forgiveness" (2001) and Of Hospitality (2000), the same structure appears in the analysis of hospitality. Unconditional hospitality, the genuine welcome of the absolute stranger, without conditions, is impossible in practice: every actual hospitality involves conditions (you are welcome here if you obey our laws, speak our language, respect our customs). But conditional hospitality that does not gesture toward the unconditional is not genuine hospitality, it is just a transaction. The tension between conditional and unconditional hospitality is undecidable and irresolvable, and that is precisely what makes genuine hospitality an ethical demand rather than a bureaucratic procedure.
In Specters of Marx (1993), written after the fall of the Berlin Wall at a moment of global triumphalism about the end of history, Derrida argues for a "hauntology" of the present: we are always inhabited by ghosts of the past (promises not kept, possibilities foreclosed, victims not mourned) and by the spectral future of justice-to-come. The living present is never fully self-present; it is always haunted by what it has excluded and by what it has not yet become. This is deconstruction as political ethics: an insistence that no present political arrangement can legitimate itself by presenting itself as the final realization of justice.