If someone goes to Israel on Vacation on Yom Tov and decides to stay in Israel to live in Middle of the second day what does he do about Melacha and davening on the Second day of Yom Tov if that very morning they Davened a Yom Tov davening?
There are Poskim that hold that even a visitor to Eretz Yisroel holds only one day, and then there are Poskim that hold that you have to be in Eretz Yisroel for a complete round of Chagim (Pesach, Shavuos, Succos - not neccessarily in this order) before you hold one day.
A friend of mine in Yeshiva, either it was first day, or second day of YomTov, decided he was staying in EY. Just like that, during YomTov, I don't think he'd even discussed it with his parents, who were categorically expecting him to return to Chutz L'oretz for University, after two years in Yeshiva in EY. The Posek told him to daven like Bnei EY, and keep all as a Ben EY from that point onwards, so mid YomTov, he was now a Ben EY. I think it may have been second day so he'd davened a chutz L'Oretz YT davening for maariv the night before, and now in the day, after lengthy discussion with the Posek, was davening as a Ben EY. He was much missed at the Yom Tov Seudoh, while he was enjoying himself learning in the Beis Hamedresh. That's about 11 years ago. He barely leaves EY and still learning there. Kein Yirbu.
When I was visting Israel to decide which community I wanted to live in, a person there suggested that I buy a room or closet in someone's house so that I can be currently owning some land in Israel. At that point, I would be only required to keep one day Yom Tov.
If they decide in the middle of Yom Tov that they want to move to Israel, in that case (if the logic works at all) you would not be able to purchase the item. I don't know what would happen if someone who keeps 1 day decided to buy you the land and then give it to you as a gift.. perhaps that could work.