The money stays in the envelopes until you pay the corresponding bill. The major problem with this method, of course, is that it was designed for a time when most transactions were handled in cash. People received pay envelopes containing bills and coins, and the folding green stuff exchanged hands for most purchases and payments. In today's world of checks, credit cards, and electronic banking, such a system is a nightmare. You would spend an enormous amount of time making cash withdrawals and deposits.
Safety is another concern.
Even worse is the fact that money sitting around in envelopes isn't working for you. Instead of just lying there, gathering dust, those funds could be out there making more money. All of these decisions are carefully documented on paper. That done, the list is carefully filed away, and the family goes out and begins spending. If the family spends under that amount, the extra is never seen or heard from again.