Fault Localization (FL) is a precursor step to most Automated Program Repair (APR) approaches, which fix the faulty statements identified by the FL tools. We present FixLocator, a Deep Learning (DL)-based fault localization approach supporting the detection of faulty statements in one or multiple methods that need to be modified accordingly in the same fix. Let us call them co-change (CC) fixing locations for a fault. We treat this FL problem as dual-task learning with two models. The method-level FL model, MethFL, learns the methods to be fixed together. The statement-level FL model, StmtFL, learns the statements to be co-fixed. Correct learning in one model can benefit the other and vice versa. Thus, we simultaneously train them with soft-sharing the models' parameters via cross-stitch units to enable the propagation of the impact of MethFL and StmtFL onto each other. Moreover, we explore a novel feature for FL: the co-changed statements. We also use Graph-based Convolution Network to integrate different types of program dependencies. Our empirical results show that FixLocator relatively improves over the state-of-the-art statement-level FL baselines by locating 26.5%-155.6% more CC fixing statements. To evaluate its usefulness in APR, we used FixLocator in combination with the state-of-the-art APR tools. The results show that FixLocator+DEAR (the original FL in DEAR replaced by FixLocator) and FixLocator+CURE improve relatively over the original DEAR and Ochiai+CURE by 10.5% and 42.9% in terms of the number of fixed bugs.