Link to one Setting featuring this.
The lowly Undead cannot be a true replacement for a living well-motivated workforce. But Undead do not tire, they do not have moods (none worth marking), they do not require pay or lunchbreaks (although a few activists start to fight for Undead rights...), and can work 24/7, if properly controled. Sadly, not only passive control is needed, so they don't start attacking all life, but also active, to ensure correct work. Undead are not very smart, and even if trained for a task, they must be instructed when to work, and when to stop, and where to work at all. Undead-Commander is a highly sought skill.
The biggest problem is sunlight. While daylight-workers are completely covered to protect from sunburn, they still feel a bit unsure and work slower. Some pranksters have also the annoying habit of removing their hood and running away, damaging this valuable property. Fines are usually the solution, prison rarely.
What YES: - Undead make good miners and excellent carriers. To a certain degree they can be lumberjacks (though they lack finesse and sometimes fall a tree on themselves). Ironically, they also make good gravediggers. Their ability to stand on guard is notorious, their stupidity also. An executioner is a good choice. For those that are tolerant, even a personal servant is available. A little enchantment extra can produce a Skeleton Scribe, a very good investment.
What MAYBE: - A messenger is an interesting possibility, but with lots of complications. A fisherman was tried out, endless patience with hook and line, with a low tolerance on water though. A bricklayer needs uninterrupted oversight, so the laid walls don't look crooked. Some can do pottery, but expect no art, only lots of similar pots. A smith can always need help, but being close to fire all day is no good for a fragile corpse. A coach-driver needs to be smart or have good imprinting, "a horse" not. A barman is also possible.
What NOT: - Undead are ill-suited to handle life and living beings. They cannot be farmers (except for plowing), as prolonged contact with plants guarantees a small harvest. For similar reasons, gardeners, herbalists, shepherds, hunters or foresters are not asked for. While smarter Undead could be cooks, this is considered a disgusting idea. Also, any artistic job is out of question.
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Legend has it, that a group of undead miners was lost at the beginning of the research for industrial purposes. Without control, the corridor they were in collapsed. Their lazy commander thought them dead. But hey "survived", and digged and digged and digged... and dig until now, for god knows how many miles deeper. And they will dig until they reach the end of the world, and fall into the emptiness. So did I hear that, don't know if it's true. But hey, you never know...