Do not forget that further damage is potentially worse.But won't the amount of current drawn (which you asked about) still depend on where in the coil the fault occurs? Higher the fault current the more likely it will take out the SC/GF protection. As far as further damaging the winding - most the time motor needs rewinding anyway even if damaged was minimized by fast overcurrent device response.
Under 25 HP unless it’s something special, throw away the motor and get a new one. The rewind cost at a reputable shop exceeds the new price unless either they aren’t a reputable shop or you need to shop around for motors.
That leaves rewinds. On newer motors they are pushing energy efficiency so much that the laminations in the core are ridiculously thin and this is causing not only rewinding issues but also a slot fault can easily damage the core. Restacking a core often again means scrapping a motor. Even on large ones.
On large motors (over 1000 HP) and under a variety of conditions that increase common mode currents another common ground fault issue is bearing currents. Currents are induced in the shaft by common mode currents and circulate either through the motor internally or returning via the frame/ground path. These always exist. Part of the conductive path is the bearings. IEEE has scientific papers going back to the 1920s referencing papers back 20 years before that so these have existed since the beginning. If the current exceeds what the bearings can tolerate it arcs through the bearing resulting in bearing fluting. This issue has always existed but normal practices keep it under control. As VFDs naturally create common mode currents the issue has returned with a vengeance.