```python
from typing import List

def mid_pair(values: List) -> List:
    """
    Return the two values standing closest to the middle of a list once it is put in order,
    the lower one first. A list of an odd length gives its middle value twice, and a list holding nothing gives two nothings.
    """
    if not values:
        return [None, None]
    
    values.sort()
    middle_index = len(values) // 2
    return [values[middle_index - 1], values[middle_index]]
```