Ah, the non-apology apology! I was very recently put in your position, although it occured in the form of a phone call, rather than a letter. My response was polite, but noncommittal. I simply thanked her for taking the time to call, but that the events in question had happened almost 2 years prior and to be quite honest, I rarely even thought of them anymore. I also told the caller I had no ill feelings toward anyone involved and I hoped there were none on their parts. Then I ended the call as quickly as possible.
Though I do see this person occasionally and we are polite, I avoid being in any social situations with her.
I think you should respond only if you are comfortable, but sometimes ignoring it might be better, especially if she is still emotionally unstable, as your friend has indicated.