Reply from Uncle Agony
The employer are required by law to cancel the work permit within 7 days since the finishing of employment.
And after his work permit is cancelled, he can only stay in Singapore for another 7 days which could not be extended again.
If his new employer could successfully apply a new work permit for him within 7 days, he do not need to go back to China, otherwise he need to wait the result in China and back to Singapore when he get the new work permit.