If I find a crumb or some piece of lint in my house and suspect it's an insect, I'll blow on it or perform some kind of action that will typically illicit a reaction under normal circumstances (e.g. touching it with my toe). If the object doesn't move, I sweep it away or continue about my day.

This "immobility" in response to my stimulus seems like an interesting way to thwart raising the interest of potential predators. This will definitely vary depending on the predator (dogs use their noses, sharks use their teeth), but are there examples of something similar to this in nature?

I originally thought of the opossum's unique behavior as an example, but feigning death doesn't seem true to the original conception of the mechanism -- an extreme version of the freeze in fight-flight-freeze reaction, if you will. Not to mention the "feigning" part is simply part of convincing the predator the possum is dead, along with a foul secreted smell, bared teeth, etc. The possum is trying to convince the predator it is DEAD rather than NOT A POSSUM, if that makes sense.