People who repeat the last syllable of what you say as your still saying it to make it seem like they knew what you were gonna say..ay

Please tell me you guys have experienced people like this. I had a friend growing up that did this. To the point where I was literally singing a song that I made up, and he repeated the last syllable and acted like he knew the words when it was made up!

Yesterday I saw a patient who did this to me for EVERY sentence I said. I honestly lost my train of thought so many times.

Has anyone else experience this?