There is a very popular story that narrates like this
It goes that a Jewish woman in Mecca who would throw garbage on the doorstep of the Prophet (peace and blessings be upon him) in defiance of his message, and one day she fell sick and could not throw the garbage, so the Prophet (peace be upon him) visited her. Then it is said that she was so amazed at his character that she realized his prophethood and accepted Islam. source
Is there any reference of this story in book of hadith or otherwise? I have seen this narrated many times in school and in every day life by others. In one of story, it even has her name.