In hyperconjugation, it is known that form an $\alpha$ hydrogen, one $\sigma$ electron goes to the corresponding carbon carbon bond, and there is apparently or practically, no bond between the hydrogen and carbon. I read in a textbook,
although one $\ce{C-H}$ bond of the alkyl is shown to be broken in each hyperconjugative structure, $\ce{H+}$ is never free from the rest of the molecule.
But then, still there is no bond. Is there any specific reason why the $\ce{H+}$ ion remains with the molecule though there is no bond attaching the ion to the rest of molecule?