Many countries have applied lockdown to suppress COVID-19, with devastating economic consequences. Here we propose exit strategies from lockdown that suppress the epidemic and provide sustainable, albeit reduced, economic activity. We use mathematical models to show that a cyclic schedule of 4-day work and 10-day lockdown, or similar variants that can be adapted in response to epidemiological observations, can in certain conditions suppress the epidemic while providing part-time employment. The cycle reduces the reproduction number R by a combination of reduced exposure time and a resonance effect where those infected during work days reach peak infectiousness during lockdown days. Throughout, full epidemiological measures need to continue including hygiene, physical distancing and extensive testing and contact tracing. Adaptive work-lockdown cycles can provide epidemic control and offer predictability to many economic sectors.