You are not allowed to stay in Singapore without valid visa. If your working visa expires and you don't get an SVP in time, you have to leave the country.
However, you will still have to fulfil your obligations from the tenancy agreement and, if there is no clause allowing early termination, you have to continue paying the rent even if you cannot stay there. After all, your visa problems are not the landlord's fault and thus he/she shouldn't be disadvantaged by it.
Of course you can talk to the landlord and try to get a mutually acceptable compromise.