Yuengling is the oldest active brewing company in the United States, having been in continuous operation since 1829. Rather than shut down in the face of the 18th amendment, owner Frank Yuengling decided to focus on brewing near-beers with less than .5% alcohol. Sales still went down and the company diversified by making dairy products like ice cream. The ice cream business kept itself afloat for the next 65 years but Yuengling went back to traditional brewing as soon as the 21st amendment was passed.

Curiously, Frank Yuengling sent president Roosevelt a shipment of their new 'winner beer' the day that the amendment was passed. Since it takes a while for beer to be brewed, the implication of this is that Yuengling had been brewing illegally in anticipation of prohibition's repeal.

Stroh's converted their breweries to make ice cream. And that's where we get Stroh's ice cream and hot fudge from.

Coor's went into the malted cereal and candy business and, in fact, had large contacts with the US Army for their cereal.

While I am by no means an authority on the matter, Yuengling is a great example. During prohibition, they stopped brewing beer and made near-beer (0.5% alcohol). They also opened up a dairy and started selling ice cream. I suspect other breweries/wineries/distilleries that survived prohibition have similar transitions.

Source: http://www.yuengling.com/faq/

I wonder if any operated illegally, providing alcohol to bootleggers. Good luck finding any sources on that for any currently operating brewery though.

I went on a tour of the Minhas brewery in Wisconsin and in addition to branching out into things like ice cream, soft drinks, and near beer it was also reasonably common to save off the alcohol removed when making non-alcoholic beer and selling that to bootleggers. It was safe, professionally made alcohol which was very valuable in Chicago.

many produced malt syrup, which could be made into beer.

Some vineyards began producing dehydrated bricks of grape must that has explicit warning of waht not to do lest you accidentally make wine.