Oh no! This is happening to me too and I have no idea what to do.
We moved in two weeks ago, and the cat came in while we were bringing things in. We put him back outside.
Since then, we've heard that his owner is on holiday, and regularly goes for 6 to 8 months of the year. He is being fed by a neighbour, but she doesn't let him in as she has a newborn.
He yowls outside our door for hours unless we let him in. We don't feed him. He doesn't ask for food. He just sleeps in here, and rubs against us. He's here now, sitting under my feet.
Last night, another neighbour came round and asked if we had him. She had heard him meowing to come in. She said she didn't mind him being here, and explained again that his owner goes away, and that she usually refuses to feed him because she thinks its cruel but the neighbour who usually feeds him is away too. She said if we wanted, we could feed him - we haven't, and we've been putting him out ten minutes before she comes, and letting him in after.
I'd be really upset if someone had my cat (I don't have one now, but grew up with them) and so last night we put him out at 5pm. He stayed right outside our front door meowing until 9pm. We went upstairs so we couldn't hear him - he continued. At 11pm, we let him in and he slept down here.
He went out at 8am this morning, possibly to toilet, and is now back in.
I don't want anyone to think we are stealing him, but he breaks my heart meowing for attention and I don't understand how anyone could leave him so often so frequently.