The largest effusive basaltic eruptions are associated with caldera collapse and are manifest through quasi-periodic ground displacements and moderate-size earthquakes1-3, but the mechanism that governs their dynamics remains unclear. Here we provide a physical model that explains these processes, which accounts for both the quasi-periodic stick-slip collapse of the caldera roof and the long-term eruptive behaviour of the volcano. We show that it is the caldera collapse itself that sustains large effusive eruptions, and that triggering caldera collapse requires topography-generated pressures. The model is consistent with data from the 2018 Kīlauea eruption and allows us to estimate the properties of the plumbing system of the volcano. The results reveal that two reservoirs were active during the eruption, and place constraints on their connectivity. According to the model, the Kīlauea eruption stopped after slightly more than 60 per cent of its potential caldera collapse events, possibly owing to the presence of the second reservoir. Finally, we show that this physical framework is generally applicable to the largest instrumented caldera collapse eruptions of the past fifty years.