I had never heard of dreams stopping and starting again when waking until DD2 had one where her friend's late brother was in her dream. He was telling DD that he was worried about someone in his family. DD woke up, went to the toilet, when she fell back to sleep her friend's brother was back in her dream talking about his relative.
DD asked me the next day should she tell her friend, I said yes, it's important, so she did. Her friend said yes they knew and had been worried about the relative too.
DD2 has always been like this, once having a dream which she told me about and the next day it happened. Other times she would dream and then she would tell me she had a commercial dream. A dream that cut into her dream and she would see herself doing something and sure enough it would happen shortly after. Simple things like someone borrowing a pencil at school, then the dream she was having would continue on after the "commercial," like a film.