Asking for examples of your work is normal. I had a friend who was asked for his pre-viva thesis for a postdoc role even though he published part of it.
Quote From DrHopeIsOutThere:
Moreover, I feel reflecting on my previous post that the reason why questions are geared towards, 'How would you approach/design said 'fieldwork example' is because its also a fishing exercise to get ideas on how to actually approach their study. I found it very strange the wording around the topic was very vague and unclear about the analytical angles of the chosen topic of study.
Yes and no. "How would you approach problem X" is a generic question across all interviews. Just talk through the problem and explain why you would do certain things. Even if means discussing rubbish ideas so that you can say why you think they are rubbish. Any PI worth their salt woul have a methodology plan already but would be open to better ideas. So it is probably more an interview question than a deliberate fishing exercise.