Troubleshooting advice for basic transistor + pro mini setup

I still have a question, and I can't find the answer online: given a common emitter transistor used a switch, what happens when the load gets too high (i.e. increasingly smaller resistance) - i.e. when the collector current reaches the max gain of the transistor?

My base has a fixed voltage (3.3V) and a fixed base resistor (1.5K), so Ic will remain at 2.6V/1.5K, and since the gain isn't infinite something will have to give... so what happens??
Will the transistor get damaged?

Thanks!
Franck