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The discovery that neutrinos are massive particles raises several questions about their properties, including their mass origin or whether they have a finite lifetime. While many terrestrial experiments are investigating some of those questions, the discovery of many different astrophysical sources has provided new avenues for exploration. By examining the data from observed astrophysical sources like the core-collapse supernova SN1987A and galaxies such as NGC1068, we will discuss the present sensitivity to some aspects related to the neutrino mass, such us their lifetime and the possibility of them being pseudo-Dirac particles. Moreover, we will explore how combining data from multiple sources can help us to identify the predicted signatures in these scenarios. Looking forward, we will also assess the future potential for understanding these properties. This evaluation will be based on the capabilities of the next generation of experiments, characterized by their large detection volume, as well as new techniques proposed to identify neutrinos.