Detect when “cursor position inside input change” in jQuery?

No, there is no event like “cursor position changed”.

But if you want to know if the cursor position changed, you can do something like this:
tested with jquery 1.7, i tested in Ie8 and chrome

var last_position = 0;
$(document).ready(function () {
    $("#my_input").bind("keydown click focus", function() {
        console.log(cursor_changed(this));
    });
});

the console.log will return when the cursor have changed.

function cursor_changed(element) {
    var new_position = getCursorPosition(element);
    if (new_position !== last_position) {
        last_position = new_position;
        return true;
    }
        return false;
}

function getCursorPosition(element) {
    var el = $(element).get(0);
    var pos = 0;
    if ('selectionStart' in el) {
        pos = el.selectionStart;
    } else if ('selection' in document) {
        el.focus();
        var Sel = document.selection.createRange();
        var SelLength = document.selection.createRange().text.length;
        Sel.moveStart('character', -el.value.length);
        pos = Sel.text.length - SelLength;
    }
    return pos;
}