WAYNESBURG — Greene County is going broke. Despite receiving millions in payouts from the natural gas industry to compensate such counties as Greene that host natural gas wells, it is struggling to balance its more than $40 million budget. This year, amid a pandemic, commissioners raised property taxes for the first time since 2010. Without major changes, county budget office projections show that Greene may not have the revenue or reserves to cover its costs by 2023. It’s a financial predicament that seemed all but guaranteed as the coal mining industry here has nearly disappeared, hollowing out the backbone of the local economy. That was, until the natural gas boom — and a massive influx of money that came with it — offered a different path.