With no sunlight, photosynthesis would stop, but that would only kill some of the plants there are some larger trees that can survive for decades without it. Within a few days, however, the temperatures would begin to drop, and any humans left on the planet's surface would die soon after. If you wanted to reach a point where Earth's gravity no longer has a hold on you, you'd have to fly out about 21 million kilometers, or 13 million miles.

Solar systems are fragile and sensitive unit of our universe. All suns in each solar system obligate to feed its planets by sending them life support, by sending them sunlight. Article Quantum Solar System

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If there was no sun, there wouldn’t be the solar system as we know it. Gravity doesn’t stop at any height. This is just elementary mechanics.

Dr Javad Fardaei and Dr Stam Nicolis thank you for your contribution to the discussion

The Earth's gravitational field extends well into space it does not stop. However, it does weaken as one gets further from the center of the Earth. The Shuttle orbits about 125 mi above the surface, roughly the distance between Jackson and Nashville. The Sun's gravitational influence extends to far distances, as evidenced by the Oort cloud out at orbital distances up to 50,000 astronomical units. But at the distance called the Hill sphere, the gravitational force of nearby stars takes over. That's at around 100,000 astronomical units. When zero gravity starts there is no such thing as zero gravity in space. Gravity is everywhere in the universe and manifests itself in black holes, celestial orbits, ocean tides, and even our own weight. With no sunlight, photosynthesis would stop, but that would only kill some of the plants there are some larger trees that can survive for decades without it. Within a few days, however, the temperatures would begin to drop, and any humans left on the planet's surface would die soon after. After the Sun exhausts the hydrogen in its core, it will balloon into a red giant, consuming Venus and Mercury. Earth will become a scorched, lifeless rock stripped of its atmosphere, its oceans boiled off. Astronomers aren't sure exactly how close the Sun's outer atmosphere will come to Earth.