```python
def camel_break(name: str) -> list:
    """
    Given a string representing an identifier with words separated by spaces,
    return a list of those words in lower case. The first word is lower cased
    if it starts with a capital, and subsequent words start with a capital
    if they do not already have a capital at the beginning.

    Examples:
    >>> camel_break("HelloWorld")
    ['hello', 'world']
    >>> camel_break("CamelCase")
    ['camel', 'case']
    >>> camel_break("snake_case")
    ['snake', 'case']
    >>> camel_break("ThisIsAValidIdentifier")
    ['this', 'is', 'a', 'valid', 'identifier']
    """
    if not name:
        return []

    parts = name.split(' ')
    result = []
    for part in parts:
        # Check if the first character is uppercase
        if part[0].isupper() and result:
            # If the previous part was also uppercase, keep the current part as is
            result[-1] += ' ' + part
        else:
            # Otherwise, convert the part to lowercase
            result.append(part.lower())
    return result
```