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Sometimes they do decay.
The neutron lasts 15 minutes; but there are nuclei that survive for milliseconds, days, decades, millenia, even billions of years. These nuclei are what we call radioactive; they are the dangerous aftermath of radiation accidents or weapons, and the tools used in smoke detectors and in fighting cancer, among other applications.
There are a number of different ways that these nuclei can fall apart, but some of them decay by having a neutron convert to a proton inside a nucleus. (We know this because the charge of the nucleus increases, and an electron comes flying out, along with an anti-neutrino.) Others even decay by having a proton convert into a neutron! (We know this because the charge of the nucleus decreases, and a positron [an anti-electron] comes flying out). Figuring out how long a given type of nucleus will survive, and how it will decay, is very complicated nuclear physics — I won’t give you a course in that here (indeed I’m no expert).
Suffice it to say that negative interaction energy among particles, combined with the conservation of energy, can change the game in a big way, making impossible certain processes that are normally possible — and vice versa.