minimum frequency in periodic components
No, there is no lower bound to the sampling theorem. Any signal $x(t)$ sampled at rate $f_\mathrm s$ can be reconstructed from its sampled version if it contains only spectral components lower than (1) $f_\mathrm{s}/2$. I.e. the frequencies contained in $x(t)$ are allowed to be as low as 0 Hz. Note however, that perfect reconstruction of $x(t)$ is only possible if an infinite number of samples $N$ has been drawn from $x(t)$. 

When it comes to spectral analysis of $x(t)$ using its sampled version $x_n = x(n/f_\mathrm s)$ the number of acquired samples $N$ plays an important role because it determines the frequency resolution of the DFT. In order to be still distinguishable the lowest frequency cannot be arbitrarily low. This is intuitively understandable as the lower the frequency the longer the period and thus the signal should be measured for a sufficently long time. Here is some further reading about DFT frequency resolution and spectral leakage

Number of FFT points required for a specific frequency resolution for an oversampled signal

FFT of sine wave not coming as expected i.e single point



(1) Actually $x(t)$ must not contain a sine wave with exact frequency $f_\mathrm s$. For an interesting discussion here on dsp.se see Nyquist Frequency Phase Shift