This paper reports on an extensive analysis of the electrical and optical properties of GaN-based high electron mobility transistors (HEMTs) biased in a non-destructive breakdown regime. By means of a number of measurements carried out with varying voltage and temperature conditions, we show that: (i) HEMTs can reach a sustainable breakdown condition, when they are biased in current-controlled mode, with a gate voltage smaller than the pinch-off voltage; (ii) when biased in sustainable breakdown, HEMTs can emit a weak luminescence signal, localized in proximity of the drain edge; (iii) the breakdown voltage (BDV) is strongly dependent on temperature. Through a careful investigation of the drain, source and gate current components, we demonstrate that breakdown originates from two different mechanisms, depending on the gate voltage: for gate voltages close to the pinch-off, breakdown current originates from the space charge injection of electrons from the source to the drain. On the other hand, for more negative gate voltages, breakdown current originates from the injection of electrons from the gate. Finally, the analysis of the temperature dependence of the breakdown current confirms that two different mechanisms significantly contribute to current conduction at high drain voltage levels.