Answer:
1-Apologize Sincerely
2-Make a promise that it won't happen again
Explanation:
In order to convey bad news, if you tend to open the message by using words that would show care and concern, you are conveying empathy through your message.
In the second part of the question, if the coworker has made a genuine mistake which is obvious and cannot be dodged and most necessarily can be tracked back, it would be a good idea for her that she apologizes for her mistakes and makes a promise to not do it again. If she denies responsibility of something so obvious, she can easily lose credibility which can lead to lay off as well.