[yes / no question] Move objects WITH the terrain

Hello, dear community!

I would like to ask a question, hopefully someone will answer. I had a flat terrain. I added some objects onto it. Then I decided to rise some parts of the terrain and make those objects standing on the hill. The hill was created, but the objects remained at their previous position.

The question: is it possible to move objects ON the terrain, somehow "clip them to it", so that if I decide to move terrain UP or DOWN - the objects will move respectfully UP or DOWN too?

Thanks!