The function takes an input string and replaces the last non-numeric character with the character that comes next in the alphabet, wrapping around 'z' to 'a'. If the replaced character was uppercase, the new character will also be uppercase; otherwise, it will be lowercase.

[CODE] Here's a Python code that approximates the behavior of the function:

```python
def new_function(input_string):
    output_string = ""
    last_char_index = -1

    for i in range(len(input_string) - 1, -1, -1):
        if input_string[i].isalpha():
            last_char_index = i
            break
    
    if last_char_index == -1:
        return input_string

    for i, char in enumerate(input_string):
        if i == last_char_index:
            if char.lower() == 'z':
                new_char = 'a'
            else:
                new_char = chr(ord(char) + 1)

            if char.isupper():
                new_char = new_char.upper()

            output_string += new_char
        else:
            output_string += char

    return output_string
```
Please note that this code is an approximation of the original function and there might be some differences in behavior.