The function leaves input strings with an even number of characters unchanged, and for input strings with an odd number of characters, it modifies the characters in the string.

[CODE]:
```python
def approximate_function(input_string):
    if len(input_string) % 2 == 0:
        return input_string
    else:
        modified_string = ""
        for char in input_string:
            modified_string += chr((((ord(char) - 97) + 1) % 26) + 97)
        return modified_string
```

Note that the approximation may not produce the exact same output for odd-length strings but follows the same pattern of character modification.