La production s'arrête, à moins que le fournisseur n'ait du stock.

From Lesson 318:Unless (à moins que)·French

Questions & Answers about La production s'arrête, à moins que le fournisseur n'ait du stock.

Why is ait used instead of a here?
The conjunction à moins que (unless) expresses a condition or restriction that is uncertain, so it always requires the subjunctive mood. ait is the subjunctive form of avoir (to have) for the third-person singular (le fournisseur).
There is an n' before ait, but the English translation doesn't say 'does not have stock'. Why is it there?
It isn't actually negative! This is called the 'ne explétif'. It is a stylistic word often used in formal French after certain conjunctions like à moins que, expressions of fear, or comparisons. It doesn't change the meaning of the sentence and is optional, though very common in written French.
Why is the reflexive s'arrête used instead of just arrête?
In French, arrêter is mostly used to mean 'to stop [something else]'. When the subject itself comes to a halt (like the production stopping), French uses the reflexive form s'arrêter.
Why does the sentence use du stock instead of just stock?
In French, you generally cannot use a noun without an article. Here, stock (inventory) is treated as an uncountable mass noun, so it takes the partitive article du to mean 'some stock' or 'inventory in general'.

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