Empirical research has shown that households in developing countries are unable to sustain current levels of consumption during and after severe health crises due to substantial increase in medical expenditure and/or loss of income. Health events are also found to have an adverse impact on nutritional status and educational attainment of household members. Thus, in this study, we investigate: who are vulnerable to welfare loss from health shocks, what are the household responses to cope with the economic burden of health shocks and if policy responses like state health insurance schemes are effective in reducing the economic vulnerability. We use self-reported measures of health shocks and coping strategies from the longitudinal survey of the ongoing Young Lives project in India [Andhra Pradesh (AP)] to identify the characteristics of vulnerable groups and perform three-level random intercept logistic regression that takes into account contextual or environmental factors. What emerges is socioeconomic status of household (determined by education, wealth, occupation and caste/religious group) and its demographic characteristics like gender of the household head and proportion of elderly and disabled members matter for outcomes related to health events. Households adopt different strategies to cope with the economic costs of ill-health; borrowing is the most widely used strategy. For credit, majority of households rely on informal sources (moneylenders, friends, relatives, etc.) and have little or no access to formal sources. However, health shock to main breadwinner leads to households adopting costly strategies like reducing consumption or sending children to work. We found no evidence that the state health insurance scheme reduced the household welfare loss from health shocks and their coping strategies. The results suggest that health insurance schemes have to be complemented with access to micro-credit and social security schemes for self-employed persons/workers in informal sector to reduce the economic burden faced by households due to health shocks.