Keep reading on 16a and you'll see that your premise isn't entirely correct. In context, when Haman was coming to find Mordechai in order to parade him around the city, Mordechai was teaching about Hilchos Kemitzah. Scared that Haman was coming to harm him, he ordered the other Rabbis to flee (though the story seems to indicate that they didn't listen) and began to daven.
אתא המן ויתיב ליה קמייהו ואוריך עד דסליק מרדכי לצלותיה אמר להו במאי עסקיתו אמרו ליה בזמן שבית המקדש קיים מאן דמנדב מנחה מייתי מלי קומציה דסולתא ומתכפר ליה אמר להו אתא מלי קומצי קמחא דידכו ודחי עשרה אלפי ככרי כספא דידי אמר ליה רשע עבד שקנה נכסים עבד למי ונכסים למי
Haman came and sat before them and waited until Mordechai finished davening. He said to them, "What are you discussing?" They said to him, "When the Temple stood, whoever would donate a Minchah would bring a fingerful of fine flour and be atoned through it." He said to them, "Your fingerful of fine flour has come and pushed aside my 10,000 silver talents." [Mordechai] said to him, "Wicked one! A slave who acquires property - to whom is the slave, and to whom is his property?!"
When the Gemara on 15a says that he was poor, it means just that - he owned nothing, as everything he owned belonged to Mordechai. He still could have had 10,000 silver talents in his possession (however it got there, as per the other answers), but it still belonged to Mordechai.