Family obligation. What have others done in similar situations?

Why in the world are you even listening to the advice and admonitions of perfect strangers to your situation.
Don't discuss anything whatsoever with them.

THIS IS NOT THEIR BUSINESS.

Why don’t they tell your sister? You’re not their messenger. Ignore people who try to make you do this or that because THEY want it done.

Provide sister’s phone number if you have it. Or her mailing address. Then tend to your own needs and those of your dad. You have enough to deal with.

As soon as someone starts to say what you SHOULD do or should NOT do stop them midsentence and say
"Thank you for your thoughts (or ideas) but I have things under control"
If they persist say
"I'm sorry, I have to go" then hang up.
If they continue then do not even reply or say "sorry" just say "I have to go now" and hang up.
Lot's of people are great at running someone else's life and those are the ones that probably are not great at running their own lives. So ignore them.

Honestly if it is an old friend and they are asking about dad why not say..."Ya know dad would love a visit, I have to go to the store how about you come by on Wednesday for a few hours so I can get some shopping done." Wanna bet the calls will slow down.

I differ with others in my opinion about this. It's not about what's between you and your sister, or peripheral people being butt-in-skies.

Your falling out with your sister should not mean that you don't try to tell her that this may be a last opportunity for her to talk to her Dad (assuming he's in hospice). You wrote that she wasn't in contact with your Dad, but that may not mean he didn't wish to be in contact with her. You don't have to have a convo with her, just pass info like where he is located and maybe a number if his room has a phone. Leave a note or a text or voicemail, or even write snailmail.

I'm thinking of people I know who would have taken advantage of a last opportunity to speak to their LO. Regrets can last forever. It would just be a magnanimous thing for you to do. The only exception is if you know for certain your Dad would not want her to be there or you think she'd show up and upset him in some negative way.

As a parent of 3 sons, I can't imagine being on my deathbed wishing to continue to nurse a grudge or be stubborn about something relational with my child.

Thanks for all of the feedback. It just so happens that someone took it upon themselves to tell her without mentioning it to me.

Regardless of what they tell you, you only need to tell her if you think you should. That's up to you. You can read the comment from Geaton and then decide if that's an appropriate reason for you and your family situation/ sister relationship to do. Give it some careful thought to decide.
If not, then,
If they think she should know, why don't they do it? They don't have to call. They could send her a letter. If they need your permission to send her a letter, than can ask you that....

So it worked itself out.

Just want to say I do believe in forgiveness. But I also believe you can forgive but not forget. You can forgive your sister for what she did but you do not have to welcome her back with open arms. You can still be leary. Forgiveness is for us anyway. My brothers, they did nothing for my Mom. I didn't like this but I forgave them for my peace of mind. I refuse to be mad at them for the rest of our lives.

"was asked if dad's surviving next of kin knew what was happening." First thought, why do they care? Not a question that usually comes up in conversation. Maybe they do know that sister is estranged thats whyvtheyvasked. Those that are "believers" also are big on forgiveness. I think the friend stepped over the line. But would it hurt to write a note to ur sister and tell her about Dad so it gives her a chance to mend fences if she wants to. Tell her if you don't hear from her, you will not contact her again even about his passing. This way you will never wonder if you should or shouldn't have.