The Clutch Slave cylinder of your Toyota Corolla is not the same as the Concentric Slave Cylinder, although the two work together. The rod from the clutch slave cylinder extends to activate the Concentric (internal) slave cylinder or release bearing. These are hydraulically operated, starting with the clutch pedal which pumps hydraulic fluid/pressure through to the master cylinder, and in turn on to the clutch slave cylinder.

Any leak of hydraulic fluid from the clutch slave cylinder of your Toyota Corolla, will result in a lack of pressure to push the rod and operate the concentric slave cylinder/release bearing. Without an operating release bearing it is not possible to disengage the clutch to change gears.