A similar scenario would play out in Britain, were there as many animals out there as the media, and some researchers suggest; which is highly unlikely as if this were the case there would be far stronger evidence for them. If we simply except all the reports presented at face value there will seem to be thousands, or at the least, many hundreds of these animals. This cannot be the case, or we would have far better proofs of their prolonged existence here. The problem is there is no real filter. And then, when the problem is looked at comprehensively, and we say to ourselves - why are they doing this? or, why don't they do that in the wild? it's almost impossible to be certain. Whereas, if we are more analytical (I mean, they are out there, there is good evidence for them!) we will have a far better chance of officially proving their presence and situation.
That being said, it is potentially possible to observe one in a town (or even a city) if the animal hasn't yet [re]adapted itself. But that animal, if it doesn't become wild very quickly, (i.e. avoid all human activities), it will be quickly recaptured, if it's lucky, or shot if it’s not!. This has happened a few times and is actually one of the better pieces of evidence for their apparently continual existence. Felicity the puma (1980) and more recently the case in Lille, France, back in September, were both examples that hadn't yet fully 'rewilded'. The juvenile captured in France and then later stolen had only been free for a day, and hadn't had any opportunity to settle into a wild environment. Although since the theft, anything's possible!.
I do expect that some breeding has naturally occurred in Britain, there is some evidence to at least suggest the possibility, but it's highly unlikely populations are sustained in this way. So, where do these animals come from? We can't keep blaming the zoos (although I think small holdings are still a concern) as today these institutions have to follow the most stringent laws in order to just remain open, they simply wouldn't risk not reporting an escape, especially one of an apex predator, to the authorities (I would know, until five years ago I was a zookeeper).
The pet trades, both legal and illegal, are the only other serious explanation.