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Expansion effects space, and since everything exists in space, expansion effects everything. The problem i think you're running into is a mistake of scale. The expansion were talking about is TINY. As good as humanity can find to fit the definition of "infintesimal". However, the universe is very, very big, and all that space adds up to compounding expansion the space in between.
In fact, once you get far enough away, all that expansion adds up to more than the speed of light. That's why we can only ever see so far into the universe, and why that limit is always growing smaller. The light emitted from stars far enough away from us will never actually make it to earth because the space in-between that star and us is expanding, right now, faster than the light can travel.
Now take all this infinitely expanding space and multiply it by a bazillion years and eventually you will expand subatomic particles so far from each other that the strong and weak nuclear forces no longer interact. Space beats energy thanks to inverse square law, so eventually space wins the universe. Everything freezes and goes dark. That's how the universe ends.
I think my point/question is a bit more subtle than a mistake of scale. It's related to Hubbles law and whether the Hubble constant is increasing over time, and if it is, whether it has an upper bound.
I'm essentially suggesting that if the Hubble constant is either decreasing or has an upper bound that is not too high, two objects that are close together and held together by sufficiently strong forces will never be "torn apart" by the expansion of the space between them. This is because the space between the objects is expanding at a rate proportional to the distance between them, as given by the Hubble constant. If the forces between the objects are sufficiently large, they will be pulled together through the expanding space faster than the space is created.
Objects accelerate away from each other, even if the Hubble constant is decreasing (I don't know if it is) because as the distance between them grows, there is more space between them expanding. Thus, two objects that are held together by some force will not accelerate away from each other if that force is large enough to pull them together faster than the space between them expands.
This is my current understanding of how space expands, please let me know if there's something fundamental I've misunderstood :)