The function takes an input string, doubles the last character, and replaces the character(s) before the last one with the character next in the alphabet if it is a letter.

[CODE]:
```python
def transform_string(s):
    new_string = ""
    for i, char in enumerate(s):
        if i == len(s) - 2 and char.isalpha():
            next_char = chr(((ord(char) - ord('a') + 1) % 26) + ord('a'))
            new_string += next_char
        else:
            new_string += char
    new_string += s[-1]
    return new_string
```

Please note that the provided code is an approximation and might not be exactly the same as the original function.