MattUK,
Every country has their own way of handling over stayers.
Where are you from and which country are you overstaying ?
If you are in Singapore and you intent to stay longer than the
exit date on your approved visa.
You should personally go down to the Immigration department and
request for an extension. Most of the time.. it will be granted,
provided you have not broken any laws.
btw.. DO NOT go to the ICA Building to get an extension if you are
still legally in Singapore and wish to stay longer than your pass
permits you!
go do it online here => e-XTEND
unfortunately, for those who have overstayed, it's a bit too
late and they should surrender themselves to the Immigration
authorities...