Inductors don't just work at single frequencies. If a specific inductor has a "rating" for a particular frequency, then that's just the more detailed specs dumbed down for easy use in a particular application.
Real inductors only work as inductors up to some maximum frequency. Above that frequency, non-ideal effects like parasitic capacitance, core loss, etc, become significant enough that they dominate the overall impedance, or at least make you take them into account.
One spec that is often quoted is the self resonant frequency. This is the frequency at which the inductance and the parasitic capacitance resonate. If you want the inductor to mostly look inductive to the circuit, you of course want to stay some margin below the self-resonant frequency.
There is no reason a inductor will stop functioning at low frequency. Any specific inductance becomes less useful, or has less effect on the circuit, as the frequency gets low, but the inductor itself still functions correctly. Inductors work just fine down to DC.
The dumbed down lower frequency limit spec may be a combination of a particular assumed use and the inductor's saturation current limit. If you apply a sine of a fixed voltage to a inductor but decrease the frequency, the current goes up. At some point, for a particular voltage applied across the inductor, the resulting current peaks are high enough to cause saturation. If the fixed voltage is known or assumed from context, then it could be said that the inductor can only be used above the frequency where the current peaks saturate the core. Or, the limit might be power dissipation in the inevitable resistance of the windings. Either way, any one inductor can't be used below a specific frequency in this particular context.