I have had personal experience with this also.
And I would recommend NOT talking to your sil directly. Do NOT give her further attention.
Support your FIL/MIL and help them get her the right help.
Help your FIL understand how he should be treating her (kindly, but firmly) and to not give attention to the cutting.
I would cut for attention, whether it was made up scenario's in my head, or when an ambulance would come and take me to hospital and care for me.
When I met my current bf, 5 years ago, he paled at what I had done and did not give me any attention what so ever about it. He had no idea how to deal with someone who did that, but his lack of attention really helped me stop doing it. I got better attention doing other nice things.
For me, I cut because I had no where to put my emotions. I would feel utter despair within my chest, trying to 'burst out' (like you might feel the sensation 'bursting with pride', but sad feelings instead).
Being taught how to deal with her emotions and not giving attention for the cutting (which would be positive reinforcement) will help your SIL get better.
But I disagree that every tom rick and harry family member should contact your sil and show their support. Not until she has seen a professional and is on the path of recovery.