The function replaces the last character of the input string with the next character in the English alphabet and appends the opposite case version of that next character. If the last character is a digit or other non-alphabetic character, it remains the same and nothing is appended.

[CODE]:
```python
def modified_string(s):
    if s[-1].isalpha():
        next_char = chr(((ord(s[-1]) - ord('a') + 1) % 26) + ord('a'))
        if s[-1].islower():
            next_char = next_char.lower() + next_char.upper()
        else:
            next_char = next_char.upper() + next_char.lower()
        return s[:-1] + next_char
    else:
        return s
```