  In-situ production of long-lived isotopes by cosmic muon interactions may
generate a non-negligible background for deep underground rare event searches.
Previous Monte Carlo studies for the GERDA experiment at LNGS identified the
delayed decays of $^{77}$Ge and its metastable state $^{77m}$Ge as dominant
cosmogenic background in the search for neutrinoless double beta decay of
$^{76}$Ge. This might limit the sensitivity of next generation experiments
aiming for increased $^{76}$Ge mass at background-free conditions and thereby
define a minimum depth requirement. A re-evaluation of the $^{77(m)}$Ge
background for the GERDA experiment has been carried out by a set of Monte
Carlo simulations. The obtained $^{77(m)}$Ge production rate is (0.21$\pm$0.01)
nuclei/(kg$\cdot$yr). After application of state-of-the-art active background
suppression techniques and simple delayed coincidence cuts this corresponds to
a background contribution of (2.7$\pm$0.3)$\cdot10^{-6}$
cts/(keV$\cdot$kg$\cdot$yr). The suppression achieved by this strategy equals
an effective muon flux reduction of more than one order of magnitude. This
virtual depth increase opens the way for next generation rare event searches.
