Once an event is named, what happens next? For Badiou, the event itself is fleeting, it appears and disappears. What matters is what you do with it afterward. He calls this fidelity (fidélité): the sustained process of working out the consequences of the event within the existing situation, deciding for each element of the situation whether it is connected to the event or not.
Fidelity is not passive loyalty. It is active, demanding, often painful work. To be faithful to the event of a revolution is to continually ask: does this decision, this institution, this compromise honor or betray what the revolution opened up? To be faithful to the event of love is not merely to feel affection but to reorganize your life and thought from the perspective of the two, the world as seen from the standpoint of this new bond. Badiou puts it with intentional hyperbole: fidelity transforms you from a merely animal being (pursuing needs and interests) into a genuine subject.
The outcome of a sustained truth procedure is a generic truth, a subset of the situation that is not definable by any of the situation's existing predicates. It is precisely indiscernible within the existing order of knowledge: you cannot specify in advance all the elements it will contain, because it is always being added to through the unpredictable work of fidelity. This is why Badiou says truth is a process, not a state: "Truth, as Badiou defines it, is the decision to be true to the unknown, and to have the fidelity to bring that unknown to fruition."
The subject, for Badiou, is not a pre-existing entity who then chooses to be faithful. The subject is constituted by the fidelity itself: you become a subject in and through the practice of working out the event's consequences. This is a radical anti-humanism: there is no rich inner self prior to the event; the subject is a local, active dimension of a truth procedure.
Badiou's ethics follows directly: the imperative is "keep going", continue the fidelity, do not betray the event by claiming it is finished, do not simulate an event where none occurred (what he calls an obscure subject), do not let the situation re-absorb the event's consequences into its old forms. Three evils correspond to three ways of failing fidelity: betrayal (giving up the procedure), simulacrum (falsely declaring an event where there is none, Badiou's example is Nazism), and disaster (persecuting those outside the truth procedure in the name of the event's universality).
Fidelity to an event is more important than the event itself. Without fidelity, we could say, the human being would lack all consistency, would become the fragmented postmodern self of arbitrary impulse and evanescent desire. Through fidelity we become subjects, because we pledge ourselves to sustain a continuity of thought and action, we stand guarantor of our own future self, even though we cannot anticipate what pressures and contingencies this future will bring.
— Alain Badiou, Being and Event (1988), summarized in Notre Dame Philosophical Reviews