The reason the Earth doesn't fall into the sun is that it's moving quickly enough that the centripetal force balances the Sun's gravity. If you escape the Earth's gravity well and give it a small push it would still have nearly as much orbital energy as the Earth and way more than Venus, which hadn't fallen into the sun either.

To slow down enough that you could fall into the sun you need to kill 30 km/s of velocity. To go fast enough to escape the solar system you only need about 15 km/s. And crashing into Jupiter is even cheaper than that.