Unfortunately, the way the "problem" is handled by many animal shelters is with the needle.
This is unavoidable for many dogs---there are not enough homes for all of the unwanted dogs and cats.
But, rescue groups are often able to find homes for animals that would be killed by shelters for space reasons.
Please don't get animal rescuers confused with people like PETA or HSUS---we are as opposed to those groups as most FReepers are. We are just softhearted people who love animals and want to help find them homes.