The woman injured on Friday by a broken bat at Boston's Fenway Park has been upgraded to a fair condition.

The family of Tonya Carpenter released a statement on Monday saying the 44-year-old is getting better after being struck in the head by a piece of Brett Lawrie's bat in the second inning of Friday's game.

"Tonya is responsive, and her condition has been upgraded from serious to fair. We would like to thank everyone for their continued support, especially the fans at Fenway Park, first responders, Boston EMS, Boston Police and her care team at Beth Israel Deaconess," the statement said.

Carpenter's injuries were initially considered life threatening.

Some players said later that they believed the injury could have been prevented with more protective netting along the foul lines.

The players union reportedly made the request for more netting during collective bargaining negotiations in 2007 and 2012, but owners balked at the request.

The Red Sox issued a statement Monday on fan safety.

"All of us with the Boston Red Sox continue to extend our best wishes to Tonya Carpenter, who was injured by a broken bat at Friday night’s game," the team's statement read.

"The wellbeing of Tonya and her loved ones are forefront in our minds.

"Major League Baseball will re-examine fan safety at ballparks, and we will fully participate in that process."