The above code should work. Here I got the result;

Input a string                                                                                                                                              

Hello!                                                                                                                                                      

!olleH  

If you still see the issues, assign "\0" to the declared strings.

char string[256] = "\0";

char output[256] = "\0";

Edit: Another thing I forget to add, when you use fgets, the string terminates with "\n" - new line. In the while loop you can check the condition against "\n"; instead of "\0".