According to this list on Wikipedia the only launches to heliocentric orbit were DSCOVR, Elon Musk's Tesla Roadster, TESS, and DART. No other SpaceX rocket went beyond a geostationary transfer orbit (GTO). In launches to GTO the second stage is typically left in a decaying elliptical low-Earth orbit, until it re-enters the atmosphere. (see e.g. here, here or here)
DSCOVR was sent to the Sun-Earth Lagrange point L1. Without station keeping this Falcon 9 second stage will have left this point and is now somewhere on the edge between heliocentric orbit and Earth's hill sphere.
Elon Musk's Tesla Roadster and the second stage that launched it are on an elliptical heliocentric orbit that crosses Mars' orbit.
TESS was launched onto a lunar flyby trajectory, after which the Falcon 9 second stages was placed in a heliocentric orbit:
For the Falcon 9 second stage, the day was not done at TESS separation as SpaceX planned to dispose the upper stage into a heliocentric orbit by firing its engine a third time to escape Earth’s gravitational influence.
- DART was sent on a collision course with an asteroid, which of course orbits around the sun:
But because DART was launched as a dedicated Falcon 9 mission, the payload along with Falcon 9's second stage was placed directly on an Earth escape trajectory and into heliocentric orbit when the second stage reignited for a second engine startup or escape burn.
Because Danuri was launched as a dedicated Falcon 9 mission, the payload along with Falcon 9's second stage was placed directly on an Earth escape trajectory and into heliocentric orbit when the second stage reignited for a second engine startup or escape burn.
At T+plus 40 minutes, with the rocket soaring over Africa, the upper stage reignited for a nearly minute-long firing to propel the payloads on a trajectory to escape the grip of Earth’s gravity and head into deep space.
- The Euclid telescope was launched to the Sun-Earth L2 point. So like DSCOVR, the upper stage will be between heliocentric orbit and Earth orbit.
Other planned SpaceX missions to heliocentric orbit are Psyche (with possibly Janus as secondary payload) and Europa Clipper.