Quantum tunneling refers to the phenomenon in which a particle can pass through a potential barrier even though its energy is lower than the barrier's height. While electron tunneling is a well-known and extensively studied phenomenon, the complete escape of an electron in its ground state from an atom due to tunneling is highly improbable.
In the context of atoms, electrons are typically found in discrete energy levels or orbitals. The ground state corresponds to the lowest energy level, which is typically very stable. The potential barrier that an electron would need to tunnel through in order to escape completely from an atom is generally quite high.
While it is theoretically possible for an electron to tunnel through a potential barrier and escape from an atom, the probability of such an event occurring is extremely low. The timescales associated with electron tunneling processes are typically very long, making it highly unlikely for a ground state electron to escape in practice.
Experimental observation of an electron in the ground state completely tunneling out of an atom would be highly challenging due to the low probability and long timescales involved. To the best of my knowledge, such an observation has not been documented in the scientific literature.