My sister (66) had a brain aneurysm 6 months ago. She was discharged from her occupational and physical therapists. How do you handle this?

You can not change her. You can change how you react.
You can not help her, she has to want to do that for herself.
Tell her that you can no longer manage her healthcare choices or her appointments. Someone in the A L facility where she is living can help her do that.
If she really can not manage her finances and if you can continue to do that OR tell her that she needs to find someone to do that as well.
If she can no longer make decisions for herself you can talk to a lawyer, best would be Elder Care Attorney and say you can no longer manage her and she needs a Guardian. The court will appoint a Guardian if there is no one you or she knows that is willing to do so

Don't try to be a fixer -- it won't work.

Sympathize with your sister, but in the end, she has made her choices and has to live with them.

After my mother's stroke, she half heartedly participated in the PT, OT, and ST. She refused to do a bunch of the exercises; batting the balloon, moving the balls from one side of the wire to the other, etc. She would roll her eyes, or look bored, or stick her tongue out and yell "No" when they wanted her to do anything she thought was stupid. Which she would also yell out.
She barely did the leg exercises and any attempt to get her up and walking was met with the same lack of interest.
She refused to participate in any of the activities, she would not eat her meals in the dining room. The only thing she actively participated in was going to the salon to have her hair washed and set every week. The rest of the time she wanted to stay in bed and watch TV.
So, you can worry yourself into a tizzy, or you can accept the fact that she is not going to participate in anything that will improve her health. With all kindness, I advise you to leave her to the decision she has made. It might not be what you or I would choose, but you can't make her do anything she doesn't want to do. Sending you a big hug because I know how hard it is to see someone just vegetated, when they could get better with just a little trying.

How very sad that at the young age of 66, your sister has basically given up on her life. Some people are content to be the victim, and allow others to have to be at their beck and call. However that doesn't mean that it has to be you who are at her beck and call.(be grateful you live many states away) You are still young as well, and have a lot of living to do, so if your sister wants to be a burden to those around her, that's on her. It doesn't mean that you have to tolerate it or embrace it.
And I know that you say that she's on an antidepressant, but that doesn't mean that that particular one is working. Anyone that I have known who suffers from depression, has had to try multiple medications before they found one that worked(and sometimes it was a combination of medications as well). It does seem like your sister is still depressed. But that's on her, not you.
You can't help or change someone that doesn't want help or to change, so quit beating yourself up, and start living and enjoying your life.
It might be best for you to limit your time talking with her, and spending time with her, since it seems to be quite upsetting for you to do so. Your sister has made her bed, and she will now have to lie in it(and probably be quite happy doing so LOL!)but that doesn't mean that you have to lie in it with her. Best wishes.

There is a "lazy gene" on my Dads side of the family and my sister inherited it. And there was no reason for it. I am not a spotless housekeeper but my house is clean. I have always made it easy for my family to keep things neat and relatively clean. My sister, food stuffed under the couch by her two year old. Dishes in the sink with mold forming. Newspapers still in wrappers all over her dining room floor. Too lazy to call the Newspaper and make them aware that former tenant no longer lives there so stop delivering. No, she never paid for them. Yes, I think there was depression involved but not diagnoised.

I know a woman who lived with a brain aneurysm for years. Raised kids, was involved in things and kept up her house. It did not stop her from living.

If she can handle her own stuff, then tell her you r no longer going to do it. How many bills can she have? She just pays her rent. Appts, she can do for herself or even the RN at the AL. Healthcare, she has Medicare and a suppliment. If she is of sound mind she can do all this. Do you have actual POA? I may keep up what ur doing but add on nothing she can do for herself. If she choses not to do it when u won't, oh well.

I am all for helping to a point. I'm the type that will go out of my way to get you the info you need on services, ect. Even to the point that I will get you the applications but after that its up to you to take advantage of the info. My friend was a "Debbie Downer". Oh poor me. Well, she lost friends with that attitude. Estranged her boys to a point and died alone. Her boys didn't visit her until she was on hospice. It was COVID so not too many visitors. Me, she had sent me a nasty message that I expected an apology for when she found out the truth. Never happened. I did send cards, books and flowers but I didn't visit. I had been taken advantage of too many times.

So, you may tell sister that she may die a very lonely person. That as she ages so do you. That you will not be putting ur life on hold for her. So, she can live her life the way she wants, just don't expect you to pick up the pieces.

We cannot make choices for others. We can only make our own choices. Your sister has made her choices. The PT and OT people recognize these choices and have had to accept them, and now you must as well. As you say she has never been a lot different. Also, there are deficits after aneurysm that can have severe repercussions that are not always curable. I am so sorry. Acceptance will make you happier, and her as well for the time she has left. I wish good luck to all. If you need help with your own acceptance then do seek help for yourself. Often specially trained Licensed Social Workers are best for these life transition changes and our adjusting around them.