A couple of interesting things...
Most people want the young cute pet, but some are very altruistic, specifically seeking out the least 'desirable' pet - say the older greyhound with three legs.
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In Canada, we also care for momma cats and kittens, until they are ready for adoption. According to the SPCA, our job is to give plenty of hugs and cuddles to them & socialise them. I'd pay to do this job...it is so enjoyable.
Our last batch of kittens, one kitten had a hard time learning to walk. It was more pushing/skating around with the front legs. With us providing support (Physically and with encouragement) within a few weeks she became almost normal.
We mentioned to the SPCA, if this animal was unadoptable, to let us know.
She said these types of pets, are the first to be adopted, just as Ed Barton mentioned.