If you put too much current through the base it will fail. 6V (forward bias) would be rather catastrophic!
I just tested a random NPN (BC550) with 90mA base current and that was still well under 1V forward.
I was curious if the transistor would explode with a directly connected higher voltage, but nothing spectacular with the one I tried - connecting a half charged lithium cell (3.8V) directly across it did nothing visible, but the transistor was quite hot and the base open circuit afterwards.