No, it couldn't be remotely stable, and erosion is not going to matter.
Even assuming the crack got formed by some very 'gentle' process that didn't destroy the planet outright, you’ve got to consider the scale of the pressures involved in a crack like that. The material making up the side of the crack has to support the weight of all the material above it. A quick google gives the breakdown pressure of stone at anywhere from tens to a couple hundred megapascals for the strongest types. On Earth, you exceed those pressures between 1 and 10km deep. That’s probably why we don’t have canyons deeper than that. Your crack is vastly deeper, so the walls of the crack have no chance of holding up.
How would that play out?
Your planet is a bit smaller than Earth but the same composition, so your surface gravity will be about half of Earth's. The gravity at the bottom of the crack will be a bit less than a third of a G. I'm too lazy to do the integration, so let's use a constant 0.4 G's for gravity in the crack.
Using that, the pressure forcing the walls together at any given point is just the weight of the stone above. Assuming a cubic meter of crack wall masses between 3000kg and 5500kg, then half-way down the crack the pressure will be between 9 billion and 16 billion pascals. At those pressures, the strength or stiffness of the walls themselves is a rounding error. 921
The walls will flow under the stress, become molten due to frictional heating, and be forced together by the pressure as fast as they can move. The pressure is enough to accelerate the walls at 300,000 G's. I'm unsure if the speed of the walls is limited like Seismic P-waves or whether you can just apply <PERSON>'s laws, but the walls will cross that 500km gap in a fraction of a second either way. It will happen sooner deeper down where the pressure is greater and the separation smaller, so the crack will seal itself up like a zipper from bottom to top.
The violence of the impact as the walls snap together will be profound. The force will send a blast wave up towards the surface, ejecting a mass of molten rock out into space.
The volume of your crack is something like 1% of the volume of your planet if I’m picturing it correctly. That means that when it snaps closed, the radius of your planet has to shrink by 0.33%. That doesn't sound like much, but it comes to an 11km drop for the entire surface of the planet. Lots of kinetic energy released. So picture a wave several km high circling the planet at several km/s until all that energy gets converted to heat..
Needless to say, this is far worse than the meteor that killed the dinosaurs. Even if conditions were earthlike before the crack closed, they won't be afterwards. 208