That isn't true. It isn't possible for something to move faster than the speed of light away from us. The speed of light is the limit of all movement for all frames of reference. Moving at the speed of light will let you catch anything, no matter what direction it is going or how fast it is going, given enough time.
If what you said was true, we couldn't even see the stuff out there in space. However, we can observe it, so therefore light from those distant galaxies is reaching us.
The reason we have a limit to how far we can see the universe is due to a different phenomenon. In short, what we see is the past. When we look at something 4 million light-years away, we see it as it was 4 million years ago. Eventually, we look out far enough in the past that it dates to the early era where space itself was opaque, blocking our sight.
There's a restriction on moving in space at speeds faster than light (or technically, sending information as "moving" is quite vague). However there is no restriction on spacetime itself moving faster than light. The problem many seem to have (and I had for quite a while) is imagining the galaxies themselves moving apart at faster than light, but this isn't what is happening.
Everywhere in the universe, spacetime is expanding at an accelerating rate. This includes the Milky Way, the local group, the solar system, even you and I. However, on the "small" scale the effect of this is negligible. any force pulling our atoms or the earth apart is easily overcome by the force of gravity, the strong force, or the electromagnetic force. This is not only allowed by relativity, it is actually predicted by it. Einstein had to cheat and add a constant to fix this, in fact (though he later claimed it was his "biggest blunder", the constant is actually still useful today to describe the acceleration of the universe.
However, over large distances this effect becomes quite profound, so that they are moving away far faster than the speed of light. The reason we can see objects beyond this horizon (the so called Hubble sphere), is the light from the stars was able to move from a region from outside this boundary to inside of it, becoming incredibly red shifted in the process.
The edge of the observable universe is the cosmic microwave background. Using any non-FTL ship, it is an impossible point to reach, because by the time we have made our way there, the edge of the observable universe (from Earth's perspective) would be even
further away. The reason light was able to make it to us at all from that time is because the universe was much smaller than it is today. And that's not even getting into the fact that there is no universal edge to the observable universe, only one that shifts based on perspective. We're all at the center of our own universe, turns out your mother was wrong.
Tiny sample size but list the number of non predatory intelligent species on erf...
Ideally, the only species that would be able to the stars is one that didn't manage to nuke themselves into oblivion. Though we don't know, which is what makes it terrifying.