I doubt it if they are still paying for it.
Well, there's a couple options there. First, if they are monthly, then they are paying for their hosting services. I have had several hosting companies, and they give you a grace period of at most a few days, and if you don't pay, your site is taken down (I had a credit card expire I was using to maintain the site and didn't realize it, that's how I know). The other option is they are paid well in advance; many hosting companies prefer to get an annual payment, and the offer a discount for the larger, upfront fees. If they are paid well through a certain time period, the hosting company doesn't know if the company is out of business - they'll keep hosting it until the contract is up, which could be a while, perhaps.
It wouldn't stay up if it hadn't been paid (or at least, I highly doubt it would). I'm pretty sure of that. But it may not have anything to do with current payments - it could be pre-paid into the future a ways.