All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The white vinegar, as well as other types of vinegars, is lawful though at some point in the manufacturing process, it may have been wine before becoming vinegar, because it was not initially manufactured as wine but as vinegar.
However, if the vinegar was manufacture to be wine, then if the vinegar was acetified by itself, it is lawful according to the view of the majority of the scholars. But if it was acetified by the intervention of a human being putting something in it, then the scholars have two opinions about it.
The first opinion:
Vinegar does not become pure and is, therefore, unlawful; this is the view of Malik, Ahmad and Ash-Shaafi'i.
The second opinion:
Vinegar becomes pure and is then lawful to be eaten; this is the view of Abu Hanifa and one narration from Ahmad because the reason of its prohibition, which is the ability of causing drunkenness, has disappeared.
Moreover, there is no difference between the natural purity emanated by Allah and the purity done through the involvement of a person such as purifying clothes or the soil (for prayers for instance). This view is narrated from 'Ataa’ and 'Amr Ibn Dinaar.
Allah knows best.