Sensor faults are non-negligible issues for soft sensor modeling. However, existing deep learning-based soft sensors are fragile and sensitive when considering sensor faults. To improve the robustness against sensor faults, this article proposes a deep subdomain learning adaptation network (DSLAN) to develop a sensor fault-tolerant soft sensor, which is capable of handling both sensor degradation and sensor failure simultaneously. Primarily, domain adaptation works for process data with sensor degradation in industrial processes. Being founded on the basic structure of deep domain adaptation, a novel subdomain learner is added to automatically learn the subdomain division, enabling DSLAN adaptable to multimode industrial processes. Notably, the subdomain structure of each sample follows a categorical distribution parameterized by output of the subdomain learner. Based on the designed subdomain learner, a new probabilistic local maximum mean discrepancy (PLMMD) is presented to measure the difference in distribution between source and target features. In addition, a generator for failure data imputation is integrated in the framework, making DSLAN handle sensor failure simultaneously. Finally, the Tennessee Eastman (TE) benchmark process and two real industrial processes are used to verify the effectiveness of the proposed method. With the fault tolerance ability, soft sensing technology will take a step toward practical applications.