come in
one thing for sure, if you legal stay status is change, means if your entry visa (or whatever kind of visa/pass) is invalid, of course you've got to leave singapore.
according to my understanding, visa/pass/permit is the reason that if they are employe you leaglly but visa/pass status is never the reason that a company will not employ somebody, except they do have reach the limit to provide ep or wp or sp. You know that there is a number limit for the companies to employ foreigners ( exculde PR). for instance, fi they employ four singaporean/PRs already, they can employ one foreigner. and if they employ 8 citizen/SPRs, then two foreigners. you can guess if 7 SC/SPR, only 1 foreigner employee can be hired.
工作VISA = ep wp sp etc...
if u want to stay here longer in order to get into the employment market, apply social visit pass =3mth or long term social visit pass = 6 mth, the details will be on ica's website.
Hope it helps.