Water broke on full term still lost the baby

Another sad things had happened. My distance cousin has lost his baby girl. So unexpected and shocked to all of us. I met the couple on chinese new year, the mummy's happily and glowing pregnant.
This time is nearly her due time when all sad things happened.
On 2 march, she felt uncomfortable, feeling a bit shiver and dizzy. So she called her doctor/gynecologic and he put her on V said she got some infection and assured her everything is ok.
On 3 march, around 9.00 am, her water broke. Her husband rushed her to hospital right away. The nurse examined her and found that she just 1cm open.
The doctor/gynea arrived at hospital on 13.00, examined her and said everything is OK, she just need to wait till her door open fully.
On 17.00, ordered from doctor by phone, she was induced by nurse and then started to have her painfully contraction.
My aunt visited her on 20.00 , she's all in pain and have regular contraction. My aunt for the doctor, the nurses assured my aunt that the doctor will arrived shortly.
But he didn't, untill the next morning, on 4 march, 7.00 the doctor arrived and after a quick examination, ordered to gave her cesarean right away.
But.....the baby was born already blue and gray, her heart is still beating though, but not able to cry and breath on her own.
Maybe because of infection, maybe because of oxygen depletion, we don't know, the doctor won't tell. But we're sad of losing a beautiful baby girl.