In Harpoon's UFO series (and other related products from other companies), the beer is bottled unfiltered, so some of the yeast carries over into the bottled beer.
As long as the beer is kept in a cool area, as not to promote the growth of the yeast, how much fermentation will occur? Aside from producing extra carbon dioxide and eventually ruining the beer, is this harmful when it proceeds over short periods?
It depends on how much sugar is present in the bottled beer.
If the beer is bottle-conditioned, a small amount of sugar is added deliberately in order to carbonate the beer. Once the yeast have eaten all the sugar, they stop producing carbon dioxide and fall to the bottom of the bottle. This is not physiologically harmful in any way, but the beer might need to be poured carefully to avoid too much yeast in the glass.
(If the beer is force-carbonated at the brewery, the yeast may contribute to the flavor of the beer, but does not produce any CO2.)
Harpoon's UFO appears to be bottle-conditioned, meaning the carbonation is produced naturally by the yeast. It's a hefeweizen, where the yeast character is actually desired - most people recommend to pour half the bottle, swirl it to suspend the remaining yeast, and then pour the rest.
(Now, home-brewed beer can be harmful if too much sugar is added at bottling - the bottles can explode and cause injury. The beer itself doesn't become harmful, though.)
The yeast have most likely stopped fermenting by the time you get the bottle, considering it's probably at least a 5 days old by that point.
The yeast stop when the fermentable sugars have been consumed. This doesn't mean they consume all sugars in the beer, but rather just those that are fermentable. Most beer has both fermentable and unfermentable sugars. This ensures there is some body still to the beer from the unfermentable sugars when fermentation is complete.
It's unlikely even if kept warm that the yeast will produce more carbon dioxide or cause any harm to the beer - there is nothing available they can metabolize, so they floc to the bottom and go dormant.
