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Real-world applications of KBQA require models to detect different types of unanswerable questions with a limited volume of in-domain labeled training data. We propose the novel task of few-shot transfer for KBQA with unanswerable questions. The state-of-the-art KBQA few-shot transfer model (FuSIC-KBQA) uses an iterative repair strategy that assumes that all questions are answerable. As a remedy, we present FUn-FuSIC – a novel solution for our task that extends FuSIC-KBQA with Feedback for Unanswerability (FUn), which is an iterative repair strategy for answerable as well as unanswerable questions. FUn uses feedback from a suite of strong and weak verifiers, and an adaptation of self-consistency for unanswerability for assessing answerability of questions. Our experiments show that FUn-FuSIC significantly outperforms suitable adaptations of multiple LLM-based and supervised SoTA models on our task, while establishing a new SoTA performance for answerable few-shot transfer as well. We have made datasets and other resources publicly available at https://github.com/dair-iitd/funfusic/.