Thanks for your question.
The short answer is that nobody knows what happened to him. There are several stories about his life which are not part of the Gospel record but they have no historical validity. All we know of Matthew is what is recorded of him in the Gospels and Acts. Here are the Bible verses that mention Matthew - either as Matthew or by his surname, Levi: Matthew 9:9; 10:3; Mark 2:14 [called Levi]; 3:18; Luke 5:27-29 [again called Levi]; 6:15; Acts 1:13
I hope you have found this helpful.
God bless and keep you,