A MOSFET is a Metal Oxide Semiconductor Field Effect Transistor. It is a switch, not a fuse (it is also an amplifier, but let's not confuse the issue). They are used in mods to allow a small (and small current capacity) switch to control very heavy currents. The "fire button" actually switches on the MOSFET, and the MOSFET switches the vape current. They add nothing to safety, aside from helping amateur modders avoid the temptation of using too-small a switch in their creations, to avoid the big, expensive and ugly switches needed for high power.
All that said, a mech is perfectly safe to vape if you have an ohmmeter, good batteries, and understand how changing the coil value also changes the amp loading on them. I, among many others here, can teach you if you are interested. I have been a mekkie since before good regulated mods offering more than 15 Watts of power became available. And in which case, you might really want to look at the Pico Squeeze I mentioned above. eLeaf swears the silly thing has electronic protection for too-low coils, although I've never had occasion to test the matter. It vapes like a mech, in other words: the coil and native battery voltage determine the applied watts, and the applied watts vary (decrease) over time as battery voltage falls. But it has short circuit protection. Kanger, FWIW, also makes a similar product, albeit I haven't tried it.