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Are you talking about single ended or push pull?
When you turn on the transistor fully, it provides a low-resistance path to a supply rail, causing that supply rail to influence the output.
When you turn off the transistor, it is high resistance, allowing the opposite supply rail to influence the output.
I had some spare time (Thanks COVID-19) and breadboarded a 2N3904 single ended class-A amplifier with an audio transformer load on the collector.
Indeed, the collector voltage exceeds B+, as shown in the attached scope waveforms.
The pink trace is the supply voltage (9v), the blue is the emitter voltage which bounds the lower swing, and the yellow is the collector voltage which goes above and below the battery voltage.
Transistor biasing is not optimized, and that is the reason the waveform will clip on the negative excursion and thus the full peak to peak excursion wasn't realized.