If one bird of the pair flew away, either to freedom, or it landed among birds that cannot be offered, one simply has to add a bird to the one that remained, and then can bring a pair. However, if the bird that flew away landed among other pairs, then we have a problem. If the remaining bird is brought, for example, as a burned offering, then its pair, the escapee, becomes a sin offering. This, in turn, makes all the birds in the group that it flew into invalid, and we lose all these offerings. To prevent this, we declare the remaining bird invalid, which makes the one that flew away also invalid. Thus we have a rule: if a bird flies away but lands with other birds, it is invalid, and makes one bird in the group that it left also invalid.
For example, if one woman had a pair of birds, the next – two pairs, and so on, until a woman with seven pairs, and a bird flew from the first woman to the second, from the second to the third, and so on, until the seventh, then each time a bird flies away, it makes one remaining birds in the group it leaves invalid. If a bird then flew back from the seventh to the sixth, from the sixth to the fifth, and so on, until the first, each woman lost two pairs of birds, except the seventh – since for her there was only one bird that flew in and left, not two.
Art: Martin Johnson Heade - Two Hummingbirds With Their Young