Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
It is authentically established in the hadiths that Isa (Jesus), peace be upon him, will kill the pigs when he descends at the end of time. This is among the actions he will undertake to abolish the distortions that have entered the religion of the Christians, including the veneration of the cross and the permitting of pork.
The Prophet ﷺ said:
“By the One in Whose Hand is my soul, the son of Mary will soon descend among you as a just ruler. He will break the cross, kill the pigs, abolish the jizyah, and wealth will become so abundant that no one will accept it.” Narrated by al-Bukhari and Muslim.
Scholars have used this hadith as evidence for the prohibition of pork and the obligation to eliminate it. They also explained that the killing of pigs by Isa, peace be upon him, serves to abolish the Christian practice of permitting them and to demonstrate the falsehood of their distorted beliefs.
Ibn Hajar, may Allah have mercy on him, mentioned that the killing of pigs when Isa, peace be upon him, descends entails abolishing the veneration of the cross and the Christian beliefs associated with it. It also indicates the prohibition of keeping and eating pigs.
If what is meant is that pigs will die or become extinct naturally, without people killing them, and that this will be one of the signs of the Hour, then we do not know of any authentic hadith establishing this.
What is authentically established in the Sunnah is that Isa, peace be upon him, will kill the pigs when he descends at the end of time, not that their natural death or extinction will be an independent sign of the Hour.
And Allah Almighty knows best.