i agree, I think she terminated by previous employer, if he / she is single and need to travel all the times, he / she won't hire a miad at home, only hire auntie to clean the house once a week.
CV and refernece letter you cannot trust, agency and training centre can make it by themselves.
if you can have interview with this maid, please ask her more things about singapore, then u can see whether she really work there before.