"The tracheotomy is a different place for the tube to go," the family source tells PEOPLE. "Everything else remains the same. It's a waiting game. The family is hoping and waiting."
The source says the procedure does not indicate a change in status.
"It's a normal procedure to have the tracheotomy because if you have a breathing tube down there for a long time, it can cause an infection," said the source.
"She is still critical and we don't know what the outcome will be," the source added. "No one is giving up on this kid."
Brown, 21, has been hospitalized since she was found unresponsive in her bathtub on Jan. 31. This past weekend, a source told PEOPLE her condition remains grim as family including father Bobby Brown and grandmother Cissy Houston keep a bedside vigil.
A second family source also confirmed to PEOPLE Thursday that Bobbi Kristina's condition "hasn't changed" – although the procedure has made an impact on her loved ones.
"There's a medical reason behind [the tracheotomy], but it's making things clear to everyone how serious this is," says the source. "Even if she wakes up, there's a possibility that this could do some damage to her vocal cords, I hear."
"This is happening because there are no other options," the source added. "If there was another way, Bobby would do it."
RadarOnline.com was the first to report the tracheotomy news.
Reporting by LIZ MCNEIL and STEVE HELLING
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