Hi,
Its immense pleasure to get back with you with another issue.
I have 2 Qns,
1.) Is there any possibility of current flow between GATE and DRAIN of MOSFET?
2.) Is there any possibility of current flow between GATE and EMITTER of IGBT?
Aside from the small leakage current, yes, there is a possibility of current flow if:
1) You've got a damaged part(!)
2) You have a high frequency signal driving the gate. There is a capacitance from Gate to Drain (Cgd) which would provide an ac current path.