This is a very interesting question that needs to be understood by distinguishing between two cases, one motivated to go wherever you want to go, and the other unmotivated to put you wherever you want to be, to see if both cases, in fact, satisfy this condition!
How far away from the Earth can't you return without power?
In fact, in the ideal state, no matter where it is placed it can return to Earth, because gravity is a long-range force, its action distance is infinite, only it will become increasingly weak, so if there is only one Earth in the universe, then this unpowered case, for example, is an unpowered lifeboat, no matter how far it is, there will always be a day back to Earth, but it may take longer.
This universe, however, has not only one Earth, but has countless planets, so that there are respective spheres of influence, and this sphere is called the Hill sphere, and the dividing point is the L1 point in the Lagrange point, as follows.
For example, the Lagrangian point L1 of the Earth-Moon system in the above figure is the boundary between the two spheres of influence. An unpowered lifeboat, as long as it leaves the Earth beyond the L1 point, then it will fall to the Moon, and if it is still within the L1 point, then it will fall to the Earth, see the above figure for the distance of this point from the Earth.
Lagrange point between the Sun and Earth is closer to the Earth, which is easy to understand, after all, the Sun and the Earth is simply not in an order of magnitude, this L1 point is located between the Earth and the Sun, 1.5 million kilometers from the Earth's location, this L1 point is a good place Oh, SOHO satellite is fixed there, you can always see the Sun, but also always see the Earth during the day.
The same reason, a ship without power once arrived here is the dividing line of the Sun-Earth tug-of-war, the power of the two sides to come here is balanced, but only a celestial linkage of the force of electricity is not balanced, sooner or later will be far from this location, drifting to where it is difficult to predict, depending on the source and direction of the disturbance.
Under infinite power, how far away from Earth can never return?
It's a question of counter-commonsense, how could it not return with unlimited power? But it really is the case that there is such a place at some definite distance from Earth, and once it reaches there, the ship, even with unlimited fuel, it will never be able to fly back to Earth.
Where is the location of the one that can't fly back? Do the math and you'll know!
The speed of light is: 299792458m/s
The Hubble constant is: 67.80±0.77(km/s)/Mpc
The distance of one second difference is: 3.2616 light years
Then this distance is: 299792.458 / 67.8 x 3.2616 x 1 million = 14421874351.221 light years
Approximately: 14,421.87 million light years
No matter how much you are loaded with fuel spaceship, as long as the flight to the Earth about 14.42 billion light years away, then do not want to return to Earth, why is this?
The expansion of the universe: a motionless can exceed the speed of light
As early as the 1920s, Hubble had already discovered that the more distant information would move away at a faster rate, thus calculating the Hubble constant, and although the numbers were a bit less precise, at least it was known that the universe was not static, while LeMayt and Friedman went a step further and derived from this cosmic expansion that the universe was born from a single primordial atom, and the concept of the Big Bang was called into being.
This was followed by the discovery of the abundance of the primordial elements in the universe and the cosmic microwave background, and the theory that the universe was born in an explosion 13.82 billion years ago, and that the afterglow of the big bang is still glowing today, while the universe has been expanding since this explosion.
What is even more surprising is that in 1998 two scientific teams also found that the universe has been expanding at an accelerated rate since about 9 billion years ago by studying the explosion of Type Ia supernovae, a conclusion that somewhat misled everyone that the universe is getting bigger and could face a thermal silence or a big tear.
But the good news is that on March 21, 2013, ESA's Planck satellite measured the most accurate Hubble constant to date as 67.80 ± 0.77 kilometers per second per million second gap (67.80 ± 0.77 km/s/Mpc), a figure that means that every 3.26 million light years the rate of expansion of the universe increases by 67.8 km/s, which is the basis for the calculation above that the universe is 14.42 billion light years away expanding beyond the speed of light.
So as soon as a vehicle reaches this position, when it intends to return to Earth, then sorry, behind it the Earth is leaving at the speed of light and will soon exceed the speed of light, and the ship in the use of existing "conventional" propulsion engines, no matter how much fuel can not let the ship accelerate to the speed of light, so it can not return.
But the ship will never reach this position, why? Expansion is not unidirectional, but every part of the universe is expanding. You see each other moving away, and they see you moving away! So that location 14.42 billion light years away, with the current engine will never reach.
The alternative, however, is for the ship to simply reach a specified point, say 10 billion light years away, and then wait there for billions of years before the rate of space expansion between this location and Earth exceeds the speed of light.
Isn't it a bit of a brain fart? But that's just an interesting answer to a boring question!