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Imagine every organism is a matter-modifying and sorting mechanism within a very large chaos.

Organisms believe their purpose is to evolve by reproduction and they're able to not wipe themselves out before every piece of matter is at its final place and or state - meaning there is no more use for any organism to interact with it. However, they are never able to change the laws of physics.

Would matter eventually be transformed into a final state in which it becomes useless to any form of life and its purpose to reproduce? What would be such a state?

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Work towards the heat death of the universe.

Your idea sounds a lot like the heat death of the universe, a hypothetical event where the universe reaches maximum entropy and no more work can be done. This will be the end of the dark era, when just photons, neutrinos, and other small subatomic particles whizzed about.

The universe won't reach this state - if it ever does - for over 10100 years. By comparison, the universe is currently about 1.3$\times$1010 years old. So the universe will go on, and on, and on, slowly winding down (for lack of a better analogy).

All your organisms have to do is simply go on living. Any work increases the entropy of a closed system, so as long as they live, they are increasing the entropy of the universe and bringing it one step closer to the heat death.

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Destined for Glory...

Pierre Teilhard de Chardin is your friend. The theology he advocated, while possibly heretical in a Catholic Context, suggests that humanity's (and by extension life's) fundamental purpose is to reach an Omega Point, a transcendent, divine state of life, whose presence somehow reverberates back through time and is perceptible to us as a divine influence.

More recent (and less religiously focused) approaches on this topic are the concepts of Singularity and Computronium, where life/artificial life refine the entire universe into a gigantic mind.

...Or Despair

For the opposite and more pessimistic view, read up on the Heat Death of the Universe and Entropy. Organisms live on neg-entropy, so our current best understanding of physics suggests a distant but inescapable final state where the entropy in the universe prevents the existence of any life or thought. This view is best summarized by the Nobel-winner physicist Steven Weinberg, who stated:

The more the universe seems comprehensible, the more it also seems pointless.

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Ah, I didn't see your edit before posting my answer! I had started mine already; I'll change it so it's less like yours. – HDE 226868 Jan 31 at 21:19

Matter is indeed modified by all life forms for the storage and production of energy. Take for example the case of green plants which store the energy of sunlight by combining water and carbon dioxide to form glucose. Herbivores convert the plant matter from one form (natural, undigested) into digested matter (wastage). Carnivores eat herbivores and use the energy stored in their body tissues (flesh) to power their own lives.

The most important thing to remember in this series of changing material forms (carbondioxide and water => plant tissue => animal tissue) is that it does not go in a straight line but loops back to the entry point. So you can say that the end product of one organism is the input for another. Dung of all animals (herbivores and carnivores) is gradually digested by bacteria and converted back into its initial components (carbon, water etc) which are once again utilized by the green plants in the manufacture of glucose.

This chain of events CAN go in a straight line with no return if you cut out the primary energy source ... the sun. Without the sun, green plants would not be able to produce glucose and then the chain of matter conversion would end at where it all started ... carnivore dung would be digested by bacteria and converted to its primary constituents, but there would be no more sunlight available to restart the whole cycle again.

So all in all, it is not a "chain" of matter conversion, but a cycle of interchanging forms where matter returns to the form where it started. If you cut out the primary energy source (stars), there would be no more living organisms left after sometime and there would be no more cyclic conversion of matter.

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You seem to be asking for our opinions or logical deductions about your science fiction, starting with astronomically general concepts. But you haven't explained them in a way that gives enough details to make sense to me.

"Organisms believe their purpose is to evolve by reproduction ..."

All organisms, or just some? It seems like a peculiar belief, to me. Also evolution isn't just something that happens as a result of reproduction, so I don't really follow what you think you're saying.

"... to not wipe themselves out before every piece of matter is at its final place and or state - meaning there is no more use for any organism to interact with it."

What? Life may modify some matter, but on Earth life survives by having a rich diversity of species which together create self-sustaining ecosystems, where their modifications tend to create cycles that balance each other, so the whole thing may fluctuate but it doesn't just convert everything to garbage (that's what short-sighted for-profit industry tends to do, but not life in general).

"Would matter eventually be transformed into a final state in which it becomes useless to any form of life and its purpose to reproduce?"

No. Especially since you ruled out life not wiping itself out by being as stupid as human industrialists. Ordinary life tends to find a sustainable balance that involves recycling, and adapts when conditions get out of balance. Without intervention from too-smart-yet-unwise industrial activity, life might live as long as there's starlight and no excessive disasters such as a huge asteroid.

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