That is why many places won't adopt anything that isn't already been spayed/neutered and current on all shots. That is one reason why the cost to adopt is so high in most places. When we were looking for a new dog a few years ago we were going to adopt form a place called Helping Hounds in Dewitt. The adoption fee was $450! It was hard for us to come up with that at the time and we ended up finding someone right before they were going to take the last "puppy" to a shelter. He was 7 months and a handful and they didn't want him. We weren't looking for a puppy, but we agreed to take him...If I knew then what I know now not...well lets just say his name fits him..."Mater"Folks are like this all the time. I always say they think everyone is like THEM! That's why they don't trust folks. I give folks the benefit of the doubt. Besides they're there to help the animals not the people. Screw the people, take the animals. If folks WILL lie do you really want them having the animals? Some of these shelter people haven't got a lick a sense.
What ticks me off, is then they let folks adopt cats or dogs WITHOUT a guarantee they'll be spayed. I say connect the shelter to the vets office who will do the surgery and if they don't show up to have them fixed go to their house and take the animal back.
You've got to understand sure it will be hard in the beginning, but as time goes by cats and dogs will be come scarce and folks will pay if they really want one.