According to the cabinet site, the Prime Minister (PM) is appointed by the President. On the PM's advice, the President appoints other Ministers from the pool of MPs.
Using a combination of several ministries' organisational charts (MCYS, MND, MOE) as a standard for the entire Singapore Government, the structure for a Ministry, in hierarchical order is as follows:
So, what would happen if a candidate (who was a Minister before the parliament was dissolved) sent to a GRC fails to win the majority votes of the GRC? The Minister would then be replaced by the President on the PM's advice (see above).
Suppose a freak result happens. Would the consequences be dire? I think not. Ministries are not a one-man show. The entire Ministry is not run by just one Minister. It is because there would still be the SMS, MS, SPS and DS assisting the new Minister.
Read what I discovered about Rowan Atkinson in one of his pre-Mr Bean roles