They can get to be a real serious problem if it is let go too long. I have not heard of this happening recently - but back in the 60's - in southern Michigan - a pack of 8 or 9 feral dogs put a farmer friend of mine up a tree and kept him there till his wife came looking for him several hours later, when they ran off. This happened several more times in the county - and then the local rod & gun club got a bunch of hunters together and set up a big drive in the woods where the dogs lived, they repeated this several times and it was very successful in cleaning them out.
I Have heard, that since then, it has become illegal to even shoot a dog you catch running deer. You have to get a game warden to do it. The dogs can be bad - but feral cats do a lot more damage to the small game and song bird populations. Any cat I see in the field is a dead cat.