Does a BJT Class A Amplifier act in Reverse Mode?
The diagram you show is a gross simplification.  In particular, it doesn't show how the transistor is kept biased so that the DC output is near the middle of its range.

The basic circuit won't work with negative inputs.  In a real circuit, the biasing provides a base level that the input both adds to and subtracts from, without the result going negative for the intended volume range.