IGBT naming question
Consider the following two states:


When \$V_{GE}\$ is less than the threshold voltage of the MOSFET, \$I_B = 0\$, and therefore \$I_C = 0\$. The IGBT is off.
When \$V_{GE}\$ is greater than the threshold voltage of the MOSFET, \$I_B\$ is set by the \$h_{FE}\$ of the BJT, and flows through the MOSFET. Therefore \$I_C = h_{FE} I_B\$; the IGBT is on.


Also, keep in mind that it is a simplified equivalent circuit. An actual IGBT is a PNPN (four-layer) semiconductor device. It's not just a BJT and MOSFET glued together in a box.