I have called Immigration dept 3 times and asked them once in person, they all confirmed that helper needs to return to home country before they will start process their new contract/visa application unless they are in one of the 4 conditions:
their previous employer terminated their contract due to financial reason
thier previous employer has emmigrate to other country
their previous employer has passed away
their previous employer has abused them
Only if one of the above reason, they can extend their visa and start apply new visa while in town (assuming they already have found a new Employer). I've just done that with my upcoming new maid and the whole process took 2.5 weeks.