The stability of the amplifier in a circuit is determined by the noise gain, not the signal gain. Most modern op amps are stable at unity gain, but some special purpose amplifiers cannot do this. Compared to standard unity-gain stabilized op amps, non-fully compensated op amps provide unique advantages, such as lower noise voltages and wider bandwidth. So, in which case should noise gain be dealt with?
Imposing noise gain can bring benefits to a variety of applications. For example, to take advantage of one or more characteristics, you may need to use a non-fully compensated amplifier below its minimum stable gain. Normally it will not work, but handling the noise gain can "fool" the amplifier into thinking it is operating at a higher gain. Another wonderful benefit of imposing high noise gain is that it improves the stability of the amplifier when driving capacitive loads.
Depending on the situation, imposing noise gain usually requires adding a resistor or a capacitor to the circuit. It may be as simple as adding a resistor between the inverting and non-inverting inputs, adding a series RC circuit between the inverting input and ground, or connecting the component in parallel with the input or gain resistor.