It takes more energy to crash into the Sun than to escape forever. Pick your starting orbit.
You are orbiting the Sun right now at 30 kilometers per second. Earth moves fast. To fall into the Sun, you need to cancel that orbital velocity entirely. If you stop dead, gravity pulls you straight in. But stopping costs almost as much energy as it takes to launch from Earth in the first place.
To escape the solar system, you don't need to stop. You just need to go a little faster. From Earth's orbit, escape velocity is 42 km/s. You're already going 30. You only need 12 more. But to hit the Sun, you need to slow from 30 to zero. That's 30 km/s of delta-v. More than twice as much.
This is why the Parker Solar Probe, which flew close to the Sun, used seven gravity assists from Venus. It didn't have enough fuel to slow down directly. It kept looping around Venus to bleed off velocity, bit by bit. Meanwhile, Voyager 2 left the solar system with a single boost from a Saturn gravity assist. It didn't even need that much fuel.
The paradox: the closer you are to the Sun, the faster you orbit, and the more energy it takes to fall in. At Mercury's distance, hitting the Sun requires more delta-v than escaping from Neptune. The Sun's gravity is strong, but it's also a moving target. You're running around it so fast that dropping in is harder than running away.
Because you're already moving sideways at 30 km/s. If you fire straight at the Sun, you keep moving sideways. You miss. You'd need to cancel your orbital velocity first, which is the hard part. It's like throwing a dart at a target while standing on a spinning carousel.
It used seven Venus flybys over seven years to gradually slow down. Each flyby shaved off a little velocity. It now dives to within 6.2 million km of the Sun's surface. It's the closest human-made object to the Sun, and it took almost a decade to get there.
Go outward first. If you fire your engine to go farther from the Sun, your orbital speed actually decreases. Once you're out past Jupiter, your sideways motion is slow enough that a small correction drops you into the inner solar system. It's the orbital mechanics version of backing out of a parking spot before pulling forward.
The Parker Solar Probe will, eventually. In 2025, after seven years of observations, it will run out of fuel and spiral into the Sun. It will burn up in the corona. It has already survived temperatures up to 1,377 degrees Celsius. The final dive will be fast and final.