No, physicists have not observed or documented a case where an electron in its ground state escapes completely from an atom due to quantum tunneling. The reason for this is that the ground state of an electron in an atom corresponds to its lowest energy state, which is typically well-confined within the atom's potential well.
Quantum tunneling refers to the phenomenon where a particle can pass through a classically forbidden barrier by exploiting the probabilistic nature of quantum mechanics. However, for an electron in its ground state, the probability of tunneling out of the atom is extremely low. The electron is tightly bound to the nucleus by the electromagnetic force, and the potential barrier that it would have to tunnel through is relatively high.
That being said, quantum tunneling is observed and studied in various other contexts, such as in radioactive decay, scanning tunneling microscopy, and tunneling in solid-state systems. But in the case of electrons in ground state within atoms, the probability of tunneling out is typically negligible, and it is highly unlikely to occur under normal conditions.
It's worth noting that electrons can transition to higher energy states or be ionized (completely freed from the atom) through other processes, such as absorption of photons or collisions with other particles. These processes are different from quantum tunneling and involve the exchange of energy and momentum between the electron and its environment.