Once there are only 19 dogs left, the number of bones will simply be reduced to (slightly more than) 18, because the prevailing ideology is that there must be 5% unemployment. (This is greatly simplified, of course, but that's the gist of it.)
Eventually you'll stop being lucky. And in any case, it's not always the same dog who gets unlucky. So yes, it is your problem, or at least it will be.