Unpowered clock divider
Use a diode to charge up a cap to 5v -0.6v = 4.4v

Now run a D FF on that 4.4v, with Qx tied to D  so you get the div_by_2 behavior.

To protect the FF, or just avoid bad behavior, use a 10K ohm resistor (brown, black, orange) in series with Clock input of FF. This is because the +5v clock signal will slightly turn on the on-chip ESD diodes and inject current into the FF substrate, with unknown affect of FF behavior. Inserting a moderate-size resistor will prevent this.