As I remember at the end of season three the spheres were destroyed, turning the Expanse back into a normal region of space, and the Xindi weapon was destroyed. Then the Enterprise was somehow sent back into to an altered history where Nazis helped by aliens were conquering the USA in World War II.
So the heroes defeated the Nazis and aliens and changed history back to what it should be in the first two episodes of the fourth season, and returned to their own time.
Then, since the expanse had been turned back into normal space where interstellar travel was easy, a lot of ships would have been heading into the expanse for exploration, trade, colonization, invasion, etc. Captain Archer could have requested permission to take the Enterprise back to rescue the Illyrians, and Archer or any or all of the crew could have publicized the plight of the Illyrians and asked for Starfleet or the Vulcan High Command or the Andorian Imperial Guard or someone or anyone to send a ship to rescue them.
Since the Enterprise was not seen rescuing the stranded Illyrians, and since no mention was made of those stranded Illyrians (or any other Illyrians) in later episodes of Enterprise - Star Trek Script Search finds no mention of Illyrians outside of "Damage" - the audience is left in the dark. Optimists can believe that Archer & his crew arranged off camera for the Illyrians to be rescued, while pessimists and cynics can believe that Archer, T'Pol, Tucker, Reed, Phlox, Hoshi, etc. all just left them stranded there to die without saying a word or lifting a finger to help them.
