Decarbonizing economies is an enormous task. Public debate often focuses on the job loss of workers in fossil industries. Why is job loss costly? Who is most affected? Can delaying transition reduce welfare costs? What other policy instruments may be available? We present a simple job search framework that calculates life-time welfare costs of job loss. We apply the model to the archetypical fossil industry - coal mining. Based on the universe of German coal employment biographies, we estimate the model and decompose welfare costs. We find that unemployment is a small factor: Higher wages and job security in coal drive welfare costs. We distinguish welfare costs by age, education and business cycle. High-educated workers aged 31-49 face highest losses. Based on a detailed demographic projection, we estimate that advancing coal exit from 2038 to 2030 increases unmitigated welfare costs by one third. Labor market policy promoting career switches rather than retirement can alleviate these welfare costs: A wage insurance scheme is estimated to reduce welfare losses by 80-99% at reasonable costs.