How did Saint Adrian become a saint?

Olympias devoted herself to the Church and was a deaconess. She led a non-cloistered group of prayerful women in her home, and devoted herself to charity and built a hospital and orphanage. She also sheltered monks expelled from Nitria, and gave away so much that her friend, Saint John Chrysostom, told her she was over-doing things a bit. In 404, due to her support of Saint John, she was persecuted, her community disbanded, her house seized and sold, and she spent the rest of her days in exile in Nicomedia. She would have been declared a saint by popular acclamation based on her life and works. No official procedure for canonization had been instituted at the time of her death.