Is there a way to recycle/use negative half of AC voltage from a rectifier?
The simple case you describe is a half-wave rectifier circuit, configured for a positive DC voltage output.  In the most basic sense, the rectifier diode acts as a switch, either allowing electrons to flow through it (on) or not (off).  During the negative half-cycles of the AC input, there is no electron flow.  It is the same as you flipping a switch on and off 60 times each second, perfectly timed for the positive half cycles.

Current (electron motion) happens only when caused by external conditions.  A battery, or a wall outlet, sits there with a potential difference (voltage) between its terminals.  If there is no connection between the terminals (an electric load like a light, motor or whatever), no electrons flow; there is no current.

Pedantic note:  "current flow" is not correct; current is the motion (flow) of electrons.  Blah blah x 10^18 electrons per second moving past a point is called 1 ampere.