According to the jQuery documentation for .keypress(), it does not catch non-printable characters, so backspace will not work on keypress, but it is caught in keydown and keyup:
The keypress event is sent to an element when the browser registers keyboard input. This is similar to the keydown event, except that modifier and non-printing keys such as Shift, Esc, and delete trigger keydown events but not keypress events. Other differences between the two events may arise depending on platform and browser. (https://api.jquery.com/keypress/)
In some instances keyup isn't desired or has other undesirable effects and keydown is sufficient, so one way to handle this is to use keydown to catch all keystrokes then set a timeout of a short interval so that the key is entered, then do processing in there after.
jQuery(el).keydown( function() {
var that = this; setTimeout( function(){
/** Code that processes backspace, etc. **/
}, 100 );
} );