(copied from IRAS website)
Q5: Does my employer need to inform IRAS if I cease employment with the company?
Yes, your employer needs to seek tax clearance by:
Informing IRAS at least one month before you cease employment or leave Singapore; and
Withholding any monies due to you until tax clearance is given or 30 days after we have received your employer's notification, whichever is earlier.
However if you are a Singapore Permanent Resident and you are merely changing jobs in Singapore, your employer does not have to seek tax clearance unless you are leaving Singapore permanently.
Q2: 关于退税的问题,我也不知道具体操作是怎样的。最好还是问IRAS. 电话或是email都会有回复的。