The function replaces the last character of the input string with a new character, where the new character has an ASCII value that is 1 more than the original character. In cases where the input string ends with a digit, the function doesn't change the last character.

[CODE]:

```python
def approximate_function(input_string):
    if input_string[-1].isdigit():
        return input_string
    else:
        new_last_char = chr(ord(input_string[-1]) + 1)
        output_string = input_string[:-1] + new_last_char
        return output_string
```

Please note that this is an approximation, and there might be subtle differences in behavior.