I have seen horrors in rehoming gone wrong, when a naive, unserious, or simply underfunded rescue gets it wrong and the dog ends up, again, with someone who inappropriate.
Every time an adoption fails, the animal acquires baggage. Sometime so much baggage that the animal is so damaged that it becomes unhomeable.
Irresponsible rehoming is as bad as irresponsible ownership. It is not fair to the animal. Rescue is there to protect the critter, punkt fertig.
After a while doing rescue you see that many people are not fit to take on a pet responsibly. Some are well intentioned but clueless, and benefit from asssessment and back up from the rescue to learn how to care for their animal. But others, sadly, simply cannot be trusted with a sentient being.
In some, perhaps many, cases it is better for the welfare of the animal to be in a well run, well regulated shelter than in an inappropriate home. The goal of rescue is to find the right home, not just any home.
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Case in point, one I heard of recently. A rather naive new Verein brought a medically fragile cat to Switzerland and did not sufficiently assess the adopter. A few days later, the adopter wanted rid, immediately. This Verein had no 'Plan B' for the poor cat - no one in the Verein could/would take him in. With no place for this poor cat to go, the Verein shipped the cat back to the country of origin... a difficult 50 hour trip. So a medically fragile cat is put through 50 difficult hours to get here, dumped with someone who couldn't care for him, then 50 difficult hours back... the cat died on the return transport. All this could have been avoided if the Verein had better adopter assessment policies in place, and a Plan B for every cross border adoption.
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Yes, there is an adoption contract. And one starts out with the assumption that adopters adhere to it. But when it is learned that an animal is at risk due to breaking the contract, pursuing legal consequences is generally wholly down to the rescue, funded by the rescue. Legal challenges can quickly eat up all the rescue's resources, funds that should better go to caring for animals. Proper assessment of adopters is a better way to go. Find the right families, not just any family.
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ETA:
I will grant you, however, that some rescues do not communicate well with prospective adopters, leaving adopters feeling put off, or put down. That is a shame, and counterproductive. Often this is because the kind of person who cares so deeply about animal welfare to get into rescue work might not have 'people skills' too. Especially when the rescue is wholly volunteer run. I'd like to see more volunteers with good 'customer facing' skills become active - and I'd like to see some rather entrenched rescue administrators acknowledging that improvement might be needed.