No, that's not how it should work; with the base floating the transistor should not conduct.
My first guess would be that you connected it wrong. It's important to note that different transistors have different pinouts, make sure you refer to the datasheet for the C8050, and not some other transistor.
If you would mistake the base for the collector then the transistor will always conduct, whether you connect the emitter at the other end, or the collector. (On their own, base-collector and base-emitter junctions act as diodes.)