Should there also be an Don't Like button on Facebook?

We are watching an episode of Secretly Pregnant.
In it a girl is talking about her previous pregnancy and the fact that her baby was stillborn.
She then had announced it on Facebook.
She was very sad that (almost) nobody reacted thus not getting any comfort.
I said to my girlfriend that it would have been a bit weird if she had gotten twenty Likes to the message of her deceased baby.
Should there be a Don’t Like button?

Side-questions: Is it a thing of the new era of social media to announce things like deaths and illnesses on sites like Facebook?
Would you use Facebook to write messages about major issues like that?