This place is my go to for unbiased opinions. 

So my question with backstory: I pay someone for childcare, and I pay them a flat rate whether the child goes or not (also pay while person goes on vacation so that they essentially have paid vacation). 
The very day schools let out due to COVID, sitter fell and broke her shoulder. She is currently in rehab after having surgery. We don't know when exactly she will be keeping children again. Which is ok because I'm working from home currently and have both my children here with me. I pay my mother in law to help me with the children when I have a lot of work to do. I feel for this person and know that this accident has affected her income. However I am not sure if I should still be paying or not. What is ethical? 

Generally people shouldn't be paid for work they don't do.  Her problem is unfortunate, but not really your problem.  That being said, I'm sure she would appreciate anything you did give her.  

I'd pay her.  And be thankful and grateful I could afford to keep paying her and supporting her in her time of need. 

How old is this lady and is the sitting money her only income?

I would give her notice that you are going to stop paying her while she is down and out.When she is well again you can pick up where you left off. If you are doing well financially and want to continue to give her something to help her out that would be kind of you.  Frankly you were already being very understanding by giving her a paid vacation because that isn't common with individuals.

If you are planning on taking your children to her when this all settles down and you go back to going to work, then you might want to continue to pay her.  If it is a financial hardship for you because you are losing income, then you can rethink that.  I never liked having to pay for daycare when I wasn't using it, but I understand that they deserve benefits like vacation pay too.

Does she keep other children besides yours?   When C was little, my aunt kept him.   I paid her whether he was with her or not.  However, this is a whole different situation.   I don't even know that Aunt Lene would have taken it. . . 

Just to answer a few questions: She is in her 60s. Has kept children in her home for 25 years or so. She had around 9 she was keeping at the time of her accident. This was her only source of income as far as I know. 
I do plan for my infant son to return to her care if she is able to return to work. When that may be we just do not know yet. 

I'm thinking of other policies of employment  (on basis of ethics). Mine for instance did not have paid maternity leave when I had my first child. I had two weeks vacation I had saved up and I did not get paid during the other three weeks I took off. 

My husband trains rope horses for a living. If he were to get bucked off and break his leg, his clients are not going to continue to pay him. 

As I mentioned, my mother in law is helping me currently and I cannot allow her to work for free, even though she probably would.  So I am paying her.

What I think I have decided to do is send her a "gift" of what would amount to a few weeks pay (as I am appreciative of her services and feel bad for her situation), and just wait for the next step. 

If she has already used up her regular vacation paid days then I wouldn't think you would be required to pay her.  Just like you said that you had to take 3 weeks of non paid maternity leave since you were out of vacation days.

That seems VERY weird to me.  Paying when it's not in use.  I realize with the covid situation, it's weird anyways. 

I can see paying for a day here or there, say your kid is sick, so you keep them home.  But to pay for weeks at a time when the person isn't doing anything is super odd for me.   

So for a 2 week vacation, you pay this person, plus you have to find your own Alternate Sitter, probably pay them as well??   Uh...I don't think so.

I realize that breaking something isn't usual and people who are employed have sick leave.  BUT...you aren't providing sick leave for the self employed!  This may be this person's only income, but that's a risk this person took being self employed.  That's what savings accounts are for and insurance. 

 I also get that you want to keep your spot for your kiddo when this person returns, but that shouldn't have to be reserved with hundreds, maybe thousands of dollars while this person is quarantined in rehab somewhere. 

Awww ok, I was thinking it was only your children that she took care of, my son and his wife were in this same situation with a sitter they had for their 6 month old when he was a baby, the sitter baby sat him till he was turning 4 years old, they payed her even when they didnt take him to her, they didnt want to lose their spot since she babysitted other childern too and was always turning away others since she could only have no more then 5 in her home, I think that was the number. But they didnt want to risk losing their spot, now hes in a per-K. She stoped all the baby sitting since she and her husband got a Divorce and had to move. If theres no risk of losing your spot with her then I would not worry about paying while shes not baby sitting, Sounds like you have done your fair share of paying while she didnt keep you child but then if theres others after her for babysitting and you could lose that spot then I would work something out.