The electron in the atom would jump out of the orbit surrounding the hydrogen nucleus. Therefore, the hydrogen atom would lose its sole electron.
Work Step by Step
When a hydrogen atom is excited from $n=1$ to $n=\infty$, it jumps from the first allowed orbit to orbit $\infty$. However, since the radius of the orbit increases as $n$ increases, the attraction between the nucleus and the electron becomes weaker as the electron moves away from the nucleus to jump to higher-state orbits. As the electron jumps to state $n=\infty$, its distance from the nucleus is now $\infty$, which is so far that the attraction between the electron and the nucleus is almost literally $0$. That means the electron is no longer in the orbit surrounding the hydrogen nucleus. Therefore, the hydrogen atom would lose its sole electron, leaving it now only with the nucleus.