What happens if a satellite runs out of fuel?

What exactly occurs when a satellite in orbit runs out of its propellant reserves? Does it simply fall back to Earth, or does it continue to orbit in some form? Are there any safety concerns for Earth-bound populations if a defunct satellite reenters the atmosphere? And, more importantly, are there any measures in place to prevent or mitigate such events? Understanding the fate of a satellite after its fuel is depleted is crucial for ensuring the safety of both space and terrestrial environments.