Her death came three weeks after Parrom was shot in the right leg during his trip home to New York to visit Williams in the hospital.
"Our thoughts and prayers are with Kevin and his family at this most difficult time," Miller said. "I have never been around a young person who has dealt with more hardship in such a short period of time than Kevin.
"I ask all Arizona Wildcat fans to join us on Saturday, Oct. 22, at 2 p.m. (PT) at our annual Red-Blue Game to be there when we introduce Kevin Parrom as a part of our 2011-12 team. He will rely on all of us here in Tucson for support in moving forward."
Miller had told reporters Wednesday that Parrom's mother was "critically ill" at a time when the player's future was uncertain because of the gunshot wound. The Arizona Daily Star reported Williams died following a battle with cancer.
The 6-foot-6 junior had returned to Tucson following the Sept. 24 shooting to rehabilitate his leg in hopes of playing one season after helping Arizona reach the Elite Eight. Police said Parrom was shot following a dispute at a residence in the Bronx.
"We're always trying to make sure he is in a good place not just physically as he makes his comeback but also emotionally, so he's in a good place there," Miller said Wednesday. "That's hard for any of us, let alone for someone who is 21 years old. We're preparing really for both, to have him and not have him. At the beginning we're preparing to not have him because he's not going to be out there, at least in practice on the short term. We're going to have to learn how to play and practice without him.
"Again, optimistically, maybe even cautiously optimistic, we hope to welcome him back to our team at some point, and we'll know more in the next two weeks, four weeks, six weeks."
Diamond Leung covers college basketball for ESPN.com and can be reached at firstname.lastname@example.org.