OP, you haven't provided much info about the medical state your relative is in.
I've been in a coma on full life support (not due to overdose or alcohol consumption) and the reason it feels like medics are saying it could go either way is because really, it could.
Nobody can tell you what the likely outcome will be and I know it's frustrating.
People in ICU can have good days and bad days, or good hours and bad hours. It's a roller coaster for the patient, their family and the staff caring for them. You should expect good news and at times, not so good news.
We don't know whether the coma is medically induced or not, what level of assistance breathing they require, what level of ventilation they require, whether there's significant damage to the liver and other organs, whether there's pre-existing physical illness or injury, whether they are responding to treatment or anything else so it really is literally impossible to judge the outcome.
Breathing support (ventilation in the case of a comatose patient) will be weaned very slowly, so when a patient appears to be doing well on ventilation, they'll turn the level of support with the breathing a tiny bit and see how the patient copes (they will still be getting ventilation, just slightly less). If they don't cope, the level will be increased again. If they DO cope, excellent, the ventilator will be set at the new slightly lower rate and this can be continued until medics feel it's safe to pause the ventilation very temporarily to see if the patient can breathe on their own. It is EXTREMELY common for a patient to need to go back on the ventilator after attempting this process. If this happens, don't assume that it means they won't recover. I went through this process several times in critical care (of course I don't remember any of it!) before I was able to breathe on my own.
Finally, if a patient starts to show progress, other support is weaned very slowly and the staff are EXTREMELY careful and quick to react if more help is needed.
Whether the fact that your relative was breathing when she was found has any bearing on likely outcome, I'm afraid I can't advise as I'm not medically trained.
I'm sorry that's not the answer you want but I hope for the best outcome for your relative.