Each sample x[n] = x(n/fₛ) records only the wave's amplitude at one instant, and once the rate drops below two samples per cycle the dots no longer determine which wave produced them.
Slide a slow sine's frequency and a sample rate and watch the lollipop samples thin out over a one-second window; the samples-per-cycle readout turns red below 2. A toggle connects the dots with straight lines for comparison with real reconstruction.