It is also possible to link against a library or executable with a
statically linked libpython, but not both with the same DLL.  In fact
building a statically linked python is currently broken on Cygwin
for other (related) reasons.

The same problem applies to other POSIX-like layers over Windows
(MinGW, MSYS) but Python's build system does not seem to attempt
to support those platforms at the moment.