It is not uncommon for neighbourhood cats to want to visit neighbour’s homes. You won’t know if an individual cat is neglected or well cared for unless you take the cat to a veterinarian which is a possibility (but unusual) if you are really concerned. However, a cat’s general appearance will give you a feeling if they are adequately cared for or, for instance, they are a stray cat struggling to cope.
However, I would be perhaps a little concerned if a cat was outside my home regularly asking to be let in. If you have a cat flap he or she will come in. It is certainly an indication that a cat either wants to explore other places and/or wants to live in a different place. As we know, domestic cats do like to choose their human companions and caretakers which can lead to disputes between neighbours.
If there is a genuine problem with a person looking after their cat and that cat is dissatisfied and wants a new home then approaching the cat’s owner may resolve the matter. It may resolve it because the cat’s owner may be uncertain as to whether they want to own a cat. They may think it’s time to relinquish or abandon their cat. Not every cat is cared for to the same extent. That response would be unlikely but you’ll have to be prepared for it and to adopt a cat if it happens.
Although there are many cat loving homes, there are those at the other end of the spectrum where the cat companion is neglected or, for instance, an individual cat is bullied by others in a multi-cat household. This might encourage a cat to find a new home.
The bottom line, however, is that domestic cats don’t understand boundaries and back or front doors. It’s all a wide open possibility to a domestic cat which is why they go to and enter other people’s homes despite being perfectly satisfied where they are. They are travelling within their home range – the area they consider theirs and which may cover many acres in an urban environment and much larger in some scarcely populated places like the Australian outback. Therefore you cannot conclude that a cat is neglected if they want to come into your home and persist in that desire. You have to ask questions, I think. Perhaps a polite and gentle conversation with the cat’s owner, as mentioned, may resolve the matter entirely.
Under exceptional circumstances a domestic cat might have been regularly visiting a home, where they were accepted, but the home owners move away and the new owners don’t want to let the cat inside. This may confuse the visiting cat. The photograph on this page shows one of these cats.