I have a friend whose been caught by immigration patrol twice, but she was physically abuse by a family member is there anything she can do to enter the US. Legally?

No... having been caught twice is unlikely they will let them here... there are however plenty of OTHER countries they can move.. not to mention other cities in their home country.

If she is abused by family member, she just needs to move out of her current home, somewhere else in her own nation.

Trying to break US law is not excused by issues at home.

Her past attempts at entry will hurt

If she is trying to re-enter US after being arrested twice the answer is NO. She should inform the authority and seek help as soon as the abuse occurred.