Automated nuclei segmentation from immunofluorescence (IF) microscopic image is a crucial first step in digital pathology. A lot of research has been devoted to develop novel nuclei segmentation algorithms to give high performance on good quality images. However, fewer methods were developed for poor-quality images like out-of-focus (blurry) data. In this work, we take a principled approach to study the performance of nuclei segmentation algorithms on out-of-focus images for different levels of blur. A deep learning encoder-decoder framework with a novel Y forked decoder is proposed here. The two fork ends are tied to segmentation and deblur output. The addition of a separate deblurring task in the training paradigm helps to regularize the network on blurry images. Our proposed method accurately predicts the instance nuclei segmentation on sharp as well as out-of-focus images. Additionally, predicted deblurred image provides interpretable insights to experts. Experimental analysis on the Human U2OS cells (out-of-focus) dataset shows that our algorithm is robust and outperforms the state-of-the-art methods.