Eve gets to look at previous output, and choose the next round of input. This is even stronger. In order to be considered high-quality algorithms must resist of these types of attacks. Here's a case where we're using cipher algorithms that were probably designed before anyone thought of the possibility of hundreds of thousands of chips on cash cards. People don't take this seriously.
People are often willing to live with it - wide range of ciphers are vulnerable.
E.g. take the key and add one bit to it. Now encrypt again, same or modified message. Turns out many implementations are not vulnerable to the attack. One problem would be. if you use a protocol where you use the key in one direction and the complement of the key in another direction. There's no shortcut that's better than trying every possible key.