After defeating Shigaraki Deku was No.1 wanted criminal in Japan with kill on sight order, so he moved to another country to start a new life.
Shigaraki had been defeated, but the consequence was dire. Various heroes killed, entire cities dismantled, casualities numbered in the millions, and public trust on heroes was at rock bottom. Not to mention the economical damage was enough to push Japan from first world to third world country.
The Japanese government need someone to blame. Someone that was not a villain; someone who must be a hero, so that the public was show that the HPSC had control of the situation and had accountability instead of blaming villains. Someone dangerous enough to make a scene about capturing and execute them, instead of having a quick arrest.
That someone was Deku.
He was the inheritor of One for All, the most dangerous quick in existence after Shigaraki and All for One vanished into history. He was too strong to be beaten down, and his heroic and unyelding mindset make him incompatible to an HPSC who needed absolute control of heroes and societies alike.
So they make him the scapegoat.
They digged up his viglante past. The decried his action against Shigiraki as illegal vigilante, blamed all the damage, death and destruction caused by Shigiraki as the result of Izuku's needless intervention that caused Shigiraki to escalate, and if Izuku was not there the heroes could have arrested the villain with little to no damage.
Izuku became Japan's most wanted criminal overnight. His friends, teachers and classmate decided to stood with him, hid him and fought to protect him as he no longer have ability to defense himself.
But Izuku saw that they are risking their life and their future, to fight against the HPSC in order to protect someone who had no value left. But he had no intention to surrender and accept judgement; he was not selfless enough to accept such outrageous demand, especially when he had done nothing wrong. So he and hos family, with the help of Ochaka and some classmate, sneak abroad a smugger ship and leave Japan in a night.
Unable to arrest Izuku, the HPSC started to smear his name further. Every secret was digged up, every storied of his life was discovered and twisted to fit the new narrative. Izuku's allies tried their best to dismiss the claim and presented the truth, but the propaganda machine of Japanese goverment was way bigger and more experienced than they could. Eventually Izuku was believed to be an agent of LoV sent to steal All Might's OfA and to sabotage UA, collaborating with Shigiraki during the War to cause untold damage until All Might sacrificed himself to stop them. His friends and allies was believed to be too hurt to accept such betrayal as real, and some started doubting themself, while other, more loud-mouthed individual like Bakugou or Eri was sent to asylum "until they accept the truth".
But Izuku didn't care. He started a new life in Europe, under a new name (and a quick to change his appearance). He worked as a cashier in a fast food chain restaurant, a simple and utterly boring life. He no longer wished to be a great hero - he could always be a hero through small kindness and helping strangers. Who need a fancy suit and flashy power, when he could do something anyone could, but did not?