If a rogue continental planet was to come too close to the Roche limit of a gas giant, it would likely be torn apart by the gas giant's gravitational forces. The Roche limit is the minimum distance from a planet where tidal forces overcome the gravitational forces holding the planet together, causing it to break apart. In this case, the gas giant's gravity would cause the rogue planet's crust to fracture and break apart, creating a debris field around the gas giant. This could potentially lead to the formation of a ring system around the gas giant as the fragments of the rogue planet are captured by its gravity.