The conductor is sized at 125% of motor rated current, per NEC motor current tables for standard sized motors that are in those tables.
The short circuit /ground fault protection can be up to 250% or if that doesn't allow motor to start can be increased even more though that shouldn't be necessary with a soft start controller. The conductor is protected from overloading by the motor overload protection.
Many VFD's and soft starters will require specific fuse types be used if the available fault current exceeds certain levels. These are fast acting fuses during short circuit/ground fault events. Should the fuse blow there is good chance your drive is also toast though. The fuse just lessened whatever fireworks show there possibly could have been in that fault event.