Understanding why you can discard left-most carry in two's complement arithmetic

Question

I have been studying binary numbers. I cannot understand why you can sometimes discard the left-most carry when adding two negative numbers. I mean, I can do some samples and see that it works, like $1101 + 1100 = -3 + -4 = 11001 = 1001 = -7$, but I don't really understand what is going on to allow this to work. Could you explain it? Thanks.