What is the ruling of the Sharia on owning a small plot of land that is not owned by anyone, next to land already owned by the person?

The permissibility of adding a piece of land to the husband's land depends on whether it is "Mawat" land that can be acquired through revitalization (ihya'). Mawat is desolate, barren land. It can be acquired through ihya' if it is not owned by anyone or if its traces are ancient and pre-Islamic (Jahiliyyah). However, land that has a specific owner cannot be acquired through ihya'. As for land that has been subject to ownership in Islam by an unnamed Muslim or Dhimmī, there is a difference of opinion, but the preponderant view is that its acquisition through ihya' is permissible. Therefore, if this piece of land is Mawat land with no owner, there is no objection to acquiring it, provided it is returned to its owner if one appears later.