No idea why you would want to do this, but writing a method to do that isn't all that hard...
public static void printlnWithIgnores(String toPrint, Set<Character> ignore) {
    for(char c : toPrint.toCharArray()) {
        if(! ignore.contains(c)) {
            System.out.print(c);
        }
    }
    System.out.println();
}
As for that happening within a string because of a character literal, I'm not sure that it's possible. Some tests:
\b (the backspace character) doesn't work 
(char)127 (the delete character) doesn't work  
That said, if your passwords can have backslashes (\) in them, that can absolutely be a problem. \ in Java is used to denote a special character, with the following character. The string "nnn" is just "nnn", but "n\nn" is 
 n
 n
Because \n represents a newline, the third n is lost.
There are many specialty characters denoted like this, but more importantly your passwords really can't have \ in them without causing issues. Either you're getting an escape character if the following character if the following character with a backslash is legal (and \1 actually is), or it won't print if it's not legal.