Everyone is concerned about their nearest and dearest. We care for, them,earn for them.
There is a little thing that I find so annoying. While it should not , but I cannot help it. So I get irritated most of the time. When someone asks that how your mother or xyz is doing ? And I tell them that unfortunately they aren't doing well. They instantly spit out the exact words "ohhh..take care of them". As if I was not doing it a moment ago. Now that you have told me to actually take care of them, From now I will make sure that I do. 
By the way , Who are you to tell me what should I do for my loved ones ? If you think you can do better, then please you are welcomed !  That's what most of the people do. We forget that the person is already so much troubled and worried and busy. People are coming to check up on the sick person, and those who cannot they are calling from far away. We have to attend every single person. Plus Make them a nice cup of tea with snacks. Have to sit with them, to watch them finish their last sip of tea and put on a fake smile on our face the whole hour. Tell them every single details that we have been telling to every person who comes by. We already have so much to do. This isn't enough for them, so they make us Listen to their Googled Home Remedies, which aren't even worth listening to. 
So by saying "take care of them" , you are just messing everything up and you are not even aware of it. I get it that there is no bad intention behind it. But it hurts the other person, who is listening this from everyone not only you. 
What I do is... I simply say " Oh that's concerning, Well I am Sure that You must be Taking Very Good Care of your xyz, I Hope They Get Well Soon. Also Do Not Forget to Take Care of Yourself too While Doing Every Possible Thing for your kith & kin." 
Just by these few words you motivate other person and make them feel good. They forget about all the tension going in their mind, at least for a few minutes. And they always remember what you tell them. 
So next time you get to know that someone's someone is not doing well, Don't forget what I said ! 
Good night!