Sure. It's called "gradual typing", and I would qualify it as trendy.
A cousin of "gradual typing" is "optional typing". In both cases, code with and without static types coexist. However, in "optional typing", the semantics of the language is completely agnostic of static types, while in "gradual typing" the semantics might consider static types, if they are available.
From the page of the course "Integrating Static and Dynamic Typing", I read they study
The design of recent languages that integrate static and dynamic typing, including Typed Racket (formerly Typed Scheme), C# 4.0, Diamondback Ruby, Haskell, Sage, and Thorn
You can add Dart to the list, which proposes optional typing as in the position paper Pluggable, Optional Type Systems.