Light is not a particle, nor is it a wave. However, under some circumstances it does behave like a particle - we even have a name for that (photon). However for purposes of this type of discussion - how it travels long distances - we need to look at the wave properties of light. The particle properties are more interaction-based.

Light moves at the speed of causality - C - so it does not experience time. Therefore light never changes. However, for distant extra-galactic objects, the space that the light is traveling through is expanding! Thus the wave property of light is stretched out as well. So what was once visible light is now so stretched out (in our reference frame) that our eyes can't detect it (that's why the night sky is black).

So yes, the light is finite. It itself experiences no change. The number of particles heading in our direction only changes when they encounter some types of mass, such as interstellar or intergalactic gad clouds.

If you want to know why light is not a particle (and also not a wave) check out the dual-slit experiments. Fascinating stuff.

The commenter is referring to the Cosmic Microwave Background (CMB). Whilst most of the universe is a dark void, if you tune a radio to a certain frequency, there's a faint, static buzz in the microwave part of the spectrum. It is heard no matter which direction you point the dish. This is a left-over from the Big Bang and started out as light but due to the expansion of space, the wavelength has increased, and that's why it's now received in the microwave part of the spectrum. There are lots of great explainers on the CMB and the history of its discovery is entertaining too. One of the easier concepts in cosmology, and one of the most important.