Deep neural network-based target signal enhancement (TSE) is usually trained in a supervised manner using clean target signals. However, collecting clean target signals is costly and such signals are not always available. Thus, it is desirable to develop an unsupervised method that does not rely on clean target signals. Among various studies on unsupervised TSE methods, Noisy-target Training (NyTT) has been established as a fundamental method. NyTT simply replaces clean target signals with noisy ones in the typical supervised training, and it has been experimentally shown to achieve TSE. Despite its effectiveness and simplicity, its mechanism and detailed behavior are still unclear. In this paper, to advance NyTT and, thus, unsupervised methods as a whole, we analyze NyTT from various perspectives. We experimentally demonstrate the mechanism of NyTT, the desirable conditions, and the effectiveness of utilizing noisy signals in situations where a small number of clean target signals are available. Furthermore, we propose an improved version of NyTT based on its properties and explore its capabilities in the dereverberation and declipping tasks, beyond the denoising task.