The function generally converts the length of an input string into its corresponding word (e.g., "four" for a 4-character input), but for certain strings (such as "eight_characters", "hello_world", and "example_string_with_underscore"), it returns an unexpected series of characters.

[CODE]:
```python
def approximate_function(input_string):
    string_length = len(input_string)
    num_to_word = {1: "one", 2: "two", 3: "three", 4: "four", 5: "five", 6: "six", 7: "seven", 8: "eight", 9: "nine", 10: "ten"}
    
    if input_string in ["eight_characters", "hello_world", "example_string_with_underscore"]:
        return "unexpected_output"
    else:
        return num_to_word.get(string_length, "undefined")
```
Please note that the 'unexpected_output' in the above code should be replaced with the actual encoded outputs observed in the run, and further investigation would be needed to identify the encoding pattern.