expressions - How to express the skill when someone does not stop working until the task is done?

Generally I hear such people referred to as having great focus.

Another term you hear a lot is dogged (typically pronounced almost like it is two words: dog ed). The word dog is sometimes used in English as a verb to describe the act of persistently chasing after someone or something. Dogged can be used as an adjective, and occasionally doggedly as an adverb.

In a more ambivalent sense, sometimes we use the metaphor or simile of a bulldog ("He's a bulldog"). This is an animal that is somewhat famous for refusing to let go of something it has bitten down on, even when you want it to.