The sad fact is: you usually know it when, half an hour after you are done whipping it, it floats in a puddle of liquid.
The problem is that it actually continues changing after you have stopped whipping. So, you really have to learn what the previous stage looks like, and stop whipping when that is reached. That's why I don't whip to really stiff peaks myself, instead I whip to soft and continue a bit, but stop before they have crossed the border to stiff, and when I let it sit, I have stiff.
This is assuming that you are making French meringue. If you are making Italian, the hot syrup stabilizes the proteins so they don't expell the water afterwards, and it reduces the volume, so whipping it longer is OK there.