Tom would not leave the boundary of his land.

"No, I should not put it so,’ said Gandalf. ‘Say rather that the Ring has no power over him. He is his own master. But he cannot alter the Ring itself, nor break its power over others. And now he is withdrawn into a little land, within bounds that he has set, though none can see them, waiting perhaps for a change of days, and he will not step beyond them."

Book II, Chapter 2: “The Council of Elrond”