In many severe recessions, people smoke and drink less because they can't afford it as much.
You have fewer car accidents as people drive less for pleasure and desperately try not to drive drunk because they cannot afford the tickets.
In the US, there was about a 0.5% improvement in mortality rates for every 1% rise in unemployment for these reasons. However, deaths from suicides and drug overdoses did go up.
And LONG term unemployment in areas has a bad effect on health, which is why life expectancy for whites with less than a college education in the US went down over the past eight years. The emotional strain of poverty, the poor diet of those on federal food subsidies (high on carbs and sugar, low on vegetables, meat), high correlation of poverty with obesity due to low exercise and bad diet, high drug use and related overdose rates ... all hurt.
So for areas that have short term economic recessions of one to three years, you get health benefits because fewer people smoke, drink, drive.
Areas which have suffered ten and twenty years of economic decline, like Appalachia in the US and former factory towns in the UK, you have massive negative effects on public health seen in declining life expectancy.