found the relevant source code, although I can't understand it:

static PyObject *
gen_send_ex(PyGenObject *gen, PyObject *arg, int exc, int closing)
{
    PyThreadState *tstate = PyThreadState_GET();
    PyFrameObject *f = gen->gi_frame;
    PyObject *result;

    if (gen->gi_running) {
        const char *msg = "generator already executing";
        if (PyCoro_CheckExact(gen)) {
            msg = "coroutine already executing";
        }
        else if (PyAsyncGen_CheckExact(gen)) {
            msg = "async generator already executing";
        }
        PyErr_SetString(PyExc_ValueError, msg);
        return NULL;
    }
    if (f == NULL || f->f_stacktop == NULL) {
        if (PyCoro_CheckExact(gen) && !closing) {
            /* `gen` is an exhausted coroutine: raise an error,
               except when called from gen_close(), which should
               always be a silent method. */
            PyErr_SetString(
                PyExc_RuntimeError,
                "cannot reuse already awaited coroutine");
        }
        else if (arg && !exc) {
            /* `gen` is an exhausted generator:
               only set exception if called from send(). */
            if (PyAsyncGen_CheckExact(gen)) {
                PyErr_SetNone(PyExc_StopAsyncIteration);
            }
            else {
                PyErr_SetNone(PyExc_StopIteration);
            }
        }
        return NULL;
    }

    if (f->f_lasti == -1) {
        if (arg && arg != Py_None) {
            const char *msg = "can't send non-None value to a "
                              "just-started generator";
            if (PyCoro_CheckExact(gen)) {
                msg = NON_INIT_CORO_MSG;
            }
            else if (PyAsyncGen_CheckExact(gen)) {
                msg = "can't send non-None value to a "
                      "just-started async generator";
            }
            PyErr_SetString(PyExc_TypeError, msg);
            return NULL;
        }
    } else {
        /* Push arg onto the frame's value stack */
        result = arg ? arg : Py_None;
        Py_INCREF(result);
        *(f->f_stacktopPP) = result;
    }

    /* Generators always return to their most recent caller, not
     * necessarily their creator. */
    Py_XINCREF(tstate->frame);
    assert(f->f_back == NULL);
    f->f_back = tstate->frame;

    gen->gi_running = 1;
    gen->gi_exc_state.previous_item = tstate->exc_info;
    tstate->exc_info = &gen->gi_exc_state;
    result = PyEval_EvalFrameEx(f, exc);
    tstate->exc_info = gen->gi_exc_state.previous_item;
    gen->gi_exc_state.previous_item = NULL;
    gen->gi_running = 0;

    /* Don't keep the reference to f_back any longer than necessary.  It
     * may keep a chain of frames alive or it could create a reference
     * cycle. */
    assert(f->f_back == tstate->frame);
    Py_CLEAR(f->f_back);

    /* If the generator just returned (as opposed to yielding), signal
     * that the generator is exhausted. */
    if (result && f->f_stacktop == NULL) {
        if (result == Py_None) {
            /* Delay exception instantiation if we can */
            if (PyAsyncGen_CheckExact(gen)) {
                PyErr_SetNone(PyExc_StopAsyncIteration);
            }
            else {
                PyErr_SetNone(PyExc_StopIteration);
            }
        }
        else {
            /* Async generators cannot return anything but None */
            assert(!PyAsyncGen_CheckExact(gen));
            _PyGen_SetStopIterationValue(result);
        }
        Py_CLEAR(result);
    }
    else if (!result && PyErr_ExceptionMatches(PyExc_StopIteration)) {
        const char *msg = "generator raised StopIteration";
        if (PyCoro_CheckExact(gen)) {
            msg = "coroutine raised StopIteration";
        }
        else if PyAsyncGen_CheckExact(gen) {
            msg = "async generator raised StopIteration";
        }
        _PyErr_FormatFromCause(PyExc_RuntimeError, "%s", msg);

    }
    else if (!result && PyAsyncGen_CheckExact(gen) &&
             PyErr_ExceptionMatches(PyExc_StopAsyncIteration))
    {
        /* code in `gen` raised a StopAsyncIteration error:
           raise a RuntimeError.
        */
        const char *msg = "async generator raised StopAsyncIteration";
        _PyErr_FormatFromCause(PyExc_RuntimeError, "%s", msg);
    }

    if (!result || f->f_stacktop == NULL) {
        /* generator can't be rerun, so release the frame */
        /* first clean reference cycle through stored exception traceback */
        exc_state_clear(&gen->gi_exc_state);
        gen->gi_frame->f_gen = NULL;
        gen->gi_frame = NULL;
        Py_DECREF(f);
    }

    return result;
}