My 41 year old daughter is in the hospital with a hgb of 2.1. her most prominent indication of this was very poor brain function...is this possible?

Extreme anemia: Wow! That's an extraordinarily low hemoglobin level; she may be lucky to be alive. Such extreme anemia certainly could cause altered mental function and other neurological symptoms, but so could the thing(s) that might cause the anemia, like blood loss, iron or folate (folic acid) deficiency, etc, etc. Discuss with her doctor(s). Good luck to her.