A star has a finite lifetime because it is burning fuel.

What is unknown is whether matter particles, e.g. electron itself, has a finite lifetime.

An unstable particle simply has a finite, indeterminate lifetime describable only by probabilities.

Not having translational symmetry also means that electronic and vibrational waves are no longer stationary states of the cuasicrystal, so they have finite lifetime.

"Since there is a finite total energy, this means a finite lifetime."

This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime.

But metastable states have finite lifetimes.

Humans are eternal angelic beings living out finite physical lifetimes on Earth (human angels).

For example, in spectroscopy, excited states have a finite lifetime.

However, all particles have a finite lifetime, as they are created and eventually destroyed by some processes.