Thanks a lot for working on this!

> _sys_shutdown is the syscall for shutdown(2) used by the socket module.

Yes, the issue with Emscripten is that a number of system calls are either not implemented or implemented but not tested. See a list we are using in https://github.com/pyodide/pyodide/blob/main/cpython/pyconfig.undefs.h (though things might have improved since it was created).

FYI, with Emscripten, the list of CPython unit tests that are currently skipped (as of Python 3.9.5) is in https://github.com/pyodide/pyodide/blob/main/src/tests/python_tests.txt some of those are due to browser VM limitations (e.g. virtual filestem by Emscripten that's not fully POSIX compliant, no processes, no sockets, async only via the browser event loop etc), others because we are not yet using threading since not all browsers support it, and some failures probably need more investigation. 

Also opened https://github.com/pyodide/pyodide/issues/2000 . Let us know if there is anything we can do help with this effort.