After Joseph died, since Jesus was busy preaching, who took care of Mary in her old age?

There is almost no information in the Gospels about what Mary was doing or where she was during the years of Jesus’ ministry. One story we do have, told by three of the four evangelists (Mark 3: 31-35, Luke 8:19-21, and Matthew 12:46-50), talks about how Mary and Jesus’ brothers come looking for him. The use of the word “brothers” here is often understood to refer to half-brothers or cousins; the New American Bible footnote for Mark 6:3 explains this in more detail. It’s very likely that these unnamed relatives were the ones who were caring for Mary while her son was doing his ministry, but we have no way of knowing for sure.