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Normally the reason for using any amplifier is to magnify the amplitude of a signal so it is large enough to be usable. It wouldn't therefore be sensible to 'sense' it while it was too small. The context of the question isn't clear but in most applications the output of the amplifier would be 'sensed' and the gain adjusted appropriately to keep that output within acceptable range. The technique is similar to 'auto range' on a DVM, if the signal is too small try making it bigger, if it is near maximum or overloading, try reducing the gain to make it smaller.
The only difference between 'variable gain' and 'programmable gain' is that the first is usually an analog method of adjusting the gain and the second does it in fixed steps with digital step selection.