Transistor Common Base configuration
When we say that the base is "grounded" in a common-base amplifier, we're talking about the AC small-signal analysis of the circuit. The key concept is that there is no signal voltage on the base terminal.

This does not mean that there's no DC bias on that terminal, if it is required for the circuit to operate. But note that the base COULD be directly connected to ground if the emitter has a negative bias (assuming NPN transistor).