But she's filed an appeal and is raising money to stop it all with the help of some people who don't even know her -- about 19,000 strangers are backing her online.
"I have a huge support system of family and friends here in North Carolina," Giordano said.
After her attorneys filed a notice of appeal Tuesday, Giordano wrote to her supporters on Facebook.
"Today WE are celebrating the wonderful news that a Fantastic Team of Attorneys have read the order and have determined that a Great INJUSTICE has been done [sic]," Giordano said. "I could never have done this alone! Thank you on behalf of myself, my children, and ALL those who have suffered INJUSTICE. WE will KEEP FIGHTING for what is RIGHT and JUST! WE ARE DOING THIS THING!!![sic]"
Court records show Giordano is out of work with no steady income and that her relationship with the children's father has been rocky, at one point both spent the night in jail after a fight.
However, their heated history hasn't stopped the cancer-stricken mother. Total strangers have opened their wallets, donating nearly $7,000 to help pay her medical and legal expenses.
"They're going to win this appeal and my kids are going to stay in Durham in their home with me, their primary caregiver their entire lives and continue to live a full and happy life here in Durham," Giordano said.
At least for a few more weeks, Giordano is supposed to give up her children on June 17.
Legal experts tell ABC11 it's unlikely she'll win an appeal.