induction question...

Amanda
I was induced with first child and it went pretty smooth for the most part. However, since being on this app I have seen people say they went in to be induced and sent home due to no progress.
This is completely new to me... I am going in to be induced on Wednesday and the thought of possibly going home with no baby just hurts my heart. I always thought if there was no success with the induction you had to have a c-section.
So how common is this exactly? Has this happened to anyone of you and you are willing to share your story? 
TIA!!