Eight items have exactly one way in, and three have a way that exists only for them
Nether Star is the only Boss Drop, Dragon Egg the only One-Time item, Command Block the only unobtainable one. Plus the eight things no chest, craft, trade or cat will ever give you.
Most items in Minecraft have several routes in — mine it, craft it, buy it, or find it in a chest. A minority have exactly one, and when that one route is closed to you the item simply is not available. Sorted by how you get them, the sources fall into eleven classes, and three of those classes contain a single item each.
The three classes with one member
Boss Drop — Nether Star. Nothing else in the game is classified this way. It comes from defeating the Wither and drops exactly one. There is no chest that contains it, no villager that sells it, and no recipe that makes it. One Wither, one star, one beacon.
One-Time — Dragon Egg. It appears once, on top of the exit portal, immediately after the first Ender Dragon kill. Respawning the dragon does not produce another. This is the only item in the game with that property, and it is why the egg is treated as a trophy rather than a resource — there is exactly one per world unless you bring in a second world.
Not Obtainable — Command Block. Available from the creative inventory or /give and by no other means. It is worth having a class for, because "you cannot get this in survival" is a different answer from "you have not found it yet", and a search that returned nothing would look like a gap in the data rather than a fact about the game.
Eight items are mob-drop-only
No chest, no crafting recipe, no trade, no fishing — kill the mob or go without:
Blaze Rod · Ghast Tear · Totem of Undying · Prismarine Shard · Shulker Shell · Wither Skeleton Skull · Turtle Scute · Breeze Rod
Six more are often listed with them and have a second way in: a Trident can come out of a trial chamber vault, Prismarine Crystals out of buried treasure, Spider Eyes out of desert pyramid chests, a Wind Charge is crafted from a Breeze Rod, and a cat you have tamed brings you Phantom Membranes and Rabbit's Feet as morning gifts.
Most of the eight are gated behind a place as much as a mob: Blaze Rods mean a Nether fortress, Shulker Shells mean an End city, Prismarine Shards mean an ocean monument, Breeze Rods mean a trial chamber. Turning difficulty down to Peaceful therefore closes off most of it in one move, which is the biggest practical consequence of that setting and rarely how it gets described.
One of the eight survives Peaceful: the Turtle Scute — a baby turtle drops one when it grows up, so no killing is involved at all. The other seven genuinely do vanish with the difficulty setting.
The two narrow sources are narrower than they look
Bartering with piglins is often described as a general-purpose gold sink, but for genuinely hard-to-source items it yields one: Ender Pearls. Everything else it gives you is obtainable more reliably somewhere else.
Fishing produces three worth fishing for, all from the treasure slot: Nautilus Shell, Saddle and Name Tag. The Saddle is the flexible one — fishing, seven kinds of chest, a ravager, a leatherworker's top trade, and since leather and iron make one, a crafting table too.
Why "one source" is the number that matters
Across the tracked items, more than half have exactly one source and only a handful have four. That skew is the useful thing to carry: for most items the interesting question is not which of several methods is fastest, it is whether the single method is open to you at all — the right dimension, the right difficulty, the right structure found.
When an item seems impossible to get, the answer is usually not a better farm. It is that its one route runs through somewhere you have not been.