Suppose someone is making a huge 50-gallon vat of cholent. Accidentally, an entire bag of milk breaks and spills into the cholent. There is more than 60x as much meat cholent as there is milk, so the milk should theoretically be batel b'shisim.
The problem is that when the milk spills into the pot, it will not automatically disperse itself evenly throughout the cholent. It will likely stay mostly in one local area. So perhaps this area of the cholent is basar b'chalav and asur. Theoretically, the entire pot would then be unkosher. Is this the case? Would stirring the pot immediately help alleviate the problem?