It's possible to design a voltage-controlled oscillator circuit with a range that extends down to zero, up to "infinity" (subject to the limits of the oscillator parts), or both, but such designs are apt to be very touchy when operated anywhere near the ends of their range. For example, if a circuit charges a cap up to 4 volts and times how long it takes to discharge down to the control voltage, and such a circuit would output 1000.0Hz when given a control voltage of 2.0 volts, then in the absence of noise or device limitations, the voltage required to get any frequency would be 4 volts/2^(1kHz/freq)--a value which will always be in the range 0 to 4 volts for any frequency, but the response would be most helpful near the middle. Starting at 1kHz and going down, for example:
Freq 1kHz/freq voltage
1000Hz 1 2.0v
500Hz 2 1.0v
250Hz 4 0.25v
125Hz 8 ~0.0156v
62.5Hz 16 ~0.0000610v
Going up, things would again start nicely but get icky at the top
Freq 1/kHz/freq voltage
1000Hz 1 2.0v
2000Hz 1/2 2.8v
4000Hz 1/4 3.36v
8000Hz 1/8 3.67v
16000Hz 1/16 3.83v
32000Hz 1/32 3.91v
64000Hz 1/64 3.957v
128000Hz 1/128 3.978v
If one were to increase the RC time constant of the circuit by about a factor of six, the resulting range might be usable (a range from 0.0156v to 3.978v would handle frequencies from about 20Hz to about 20KHz) but the circuit would be more sensitive than ideal near the edges of its frequency range.