Unfortunately not. Sound pressure hits the wall and vibrates the wall or floor and everything that they're connected to. A single layer of subfloor (plywood) or sheetrock (drywall) stops more sound than any piece of foam could ever hope of doing. If you put a piece of foam up to your mouth and moaned… everyone standing on the other side of that foam would hear you almost just as well. That being said, even if the room were 100% covered in foam an outsider would still hear it nearly as good as if you had none. Maybe 15% less.

Foam works better for the people in the room because the effect of the foam is doubled. Sound passes through foam (loses some energy), bounces off the drywall and then passes through the foam again (losing more energy) before it gets back to your ear. For someone outside the room though they only need the sound to pass through the foam a single time to hit the drywall and or floor, that's why they hear it regardless.

Construction actually works because it's making the wall thicker and heavier. Then it takes more force (louder sounds) to vibrate the thing the sound is hitting (such as walls and floor) to make the floor even start to move. The effect of that is that basically it means that the insider needs to make louder sounds for the outsider to hear it. So.. yea, unfortunately nothing can stop this problem. Nothing economical at least.