I'm going to go out on a limb here and say that this other person has already ended the friendship.
Respond to any communication she makes politely, but don't initiate any communications of your own. Don't make any promises or commitments to her.
If this leaves a hole in your life—for which I would not blame you—go ahead and find someone else to fill it. (If you want to know the best way to fill that hole, it's another topic for another question.)
You want to know what to do. (Full disclosure: I am an adult child of an alcoholic father, so I understand your struggle to some degree.)
Step One: Commit to moving on, no matter what.
If I were in your position, the only closure I would need is my own commitment to ending the relationship. Any closure in which she accepts your decision requires her to be reasonable, and this is completely beyond your power. As a now-disgraced comedian once said:
I don't know the recipe for success, but the recipe for failure is trying to please everybody.
You have no control over how she will respond to your decision. You may be letting this uncertainty stop you from doing what is best for you. That needs to stop:
- You do NOT need her permission to end the relationship.
- You do NOT owe her an explanation for ending the relationship.
- You do NOT have to correct her if she is wrong about something (assuming, of course, that you have not misled her about anything).
If you concede any of these points, you grant her the power to keep you dangling; she will withhold her permission, ignore your explanations, and refuse all correction, just to keep things going. You cannot win that game—she will move goal posts faster than you can run—but you can and should refuse to play it.
Step Two: Tune her out.
As far as social media goes, adjust your settings so that her social media activity no longer shows in your feed. In Facebook, for instance, simply stop following her posts. If she sends you private messages, you should be able to tell whether they are genuine requests for help, or an attempt to hurt you or assert control; answer the former if you want to, delete the latter. If you have social media links to other people that exist only because they are her friends, filter them out as well, so that her activity in their feeds doesn't show up in yours.
If she knows your phone number, you may find it necessary to block her calls and texts.
Step Three: Let sleeping dogs lie.
As far as informing her of this, I recommend that you simply do nothing.
Even if your message ending the friendship is 100% truthful and 100% respectful, some people are triggered by anything that smacks of criticism, especially if it touches on a problem of which they are in denial.
If you say nothing to her, then at a later point decide to resume the relationship, you will not be in the position of having to unsay something.
If you send her any message, she may misunderstand it, and it will be difficult to correct the situation. Or she may correctly understand the message, but will lash out because your message reminds her of something she's trying to avoid.
So the best explanation is to provide no explanation at all. As the saying goes,
A wise man once said nothing.
Step Four: Remain firm.
She may do the social media equivalent of yelling and screaming and stamping her feet, but she can't do it forever, and if anyone who isn't enabling her behavior asks you about it, you can let them in on the truth. The drama will pass.
Epilogue: Remain open to genuine repentance.
It may be that in time some event will leave her with no choice but to accept that she has a problem. If she contacts you and says that she has given up drinking and wants to mend fences, take her at face value and do what you can to help her stay on the wagon. That will also be a good time to tell her that you can only be friends while she's sober.