That's the magic of action potentials. As sodium ions (+1 charge) propagate, they dissipate throughout the cytosol and sometimes leak out of the cell membrane, but they also trigger their own influx of regenerative current by opening voltage-gated ion channels on the cell membrane. Think of it as a "signal repeater".
As long as the initial stimulus is strong enough to trigger an action potential, the signal propagates all the way from the nerve ending to the central nervous system, and whatever response the CNS cooks up always makes it all the way to all the muscles it intends to trigger. Stated another way, the peripheral and central nervous system have enough of these signal repeaters for any signal to travel anywhere.
As long as the initial stimulus is strong enough to trigger an action potential, the signal propagates all the way from the nerve ending to the central nervous system, and whatever response the CNS cooks up always makes it all the way to all the muscles it intends to trigger. Stated another way, the peripheral and central nervous system have enough of these signal repeaters for any signal to travel anywhere.