Static AND Dynamic Typing?

Is it possible to create a language where it's statically typed (preferably with inference) by default, but can drop to dynamic typing for bits where you need it. I seem to remember someone saying this wouldn't work. Can anyone explain why?

>>11
Static typing is indispensable when you're modifying code and APIs
Only not

letting the compiler
Fail

and editor
Even more fail, gb2/Visual Studio, IDEfag

Real code is maintained
And especially because of that, you don't want to shoot your foot with unnecessary particularization.