The COVID-19 pandemic exhibits intertwined epidemic waves with anomalous fade-outs characterized by persistent low prevalence. These long-living epidemic states complicate epidemic control and challenge current modeling approaches. Here we introduce a modification of the Susceptible-Infected-Recovered model in a meta-population framework where a small inflow of infected individuals accounts for undetected imported cases. Focusing on a regime where this external seeding is so small that cannot be detected from the analysis of epidemic curves, we find that outbreaks of finite duration percolate in time, resulting in overall low but long-living epidemic states. Using a two-state description of the local dynamics, we can extract analytical predictions for the phase space. The comparison with epidemic data demonstrates that our model is able to reproduce some critical signatures observed in COVID-19 spreading in England. Finally, our findings defy our understanding of the concept of epidemic threshold and its relationship with outbreaks survival for disease control.