Over the past few years, incentive- or price-based demand response programs targeting residential energy demand have become increasingly popular in high-income countries. Such programs aim to shift energy demand from times when there is limited supply to times of abundance, in order to ensure stable grid operation. However, despite their cost-effectiveness, these schemes have gained little traction in low-income countries, where the amount of residential flexibility cannot be accurately quantified due to a lack of existing demand response studies, and grid operators continue to rely on the blunt instrument of grid outages to manage demand. In this paper, we propose a framework to quantify the flexibility using existing grid outages. Applied to high-resolution sub-metered data from 42 households in Lahore (Pakistan), we show that the proposed method is able to quantify available flexibility at the residential or feeder-level in an automated manner. The proposed method can also be used to evaluate the efficacy of grid outages as a strategy to shift or curtail demand, which can in turn be used to design better demand response schemes. Our results provide evidence that load-shedding causes significant rebound peaks due to shifted demand, while overall energy demand is actually increased rather than curtailed due to the mitigation strategies adopted by households. The paper concludes with the most important policy implications, especially with the rapid proliferation of distributed solar PV systems.