I came up with this technique many years ago when we were doing almost exclusively apartments and other rental property. The indentations become an even bigger issue when the rooms are vacant. The problem increased as the less resilient polyester and polypropylene became more common. There were so many comments/complaints, I felt like I had to do something.
Anyway, take a damp towel, as in dye stain removal, and a steam iron. Water in the iron and steam on. Heat the spot up, get the pile and backing soft and pliable. When the spot is nice and hot pull up in the center to "re-set" the backing. Then I used a Handi-Groomer to re-set the pile. Let it cool and firm back up. In other words, heat that plastic, reshape it to the position you want and cool it. Some come out perfect, others, not quite as perfect. Still, this works better than anything else I've tried.
As far as the pad depression, it's still there but is usually not a problem. Once the backing cools and firms back up it seems to hold its shape, even with the void underneath.
It can be time consuming so charge as you see fit.