If it's actually unsupported, it could be a bargain.
Maybe OP should approach the company and offer to buy it, rights/source code etc, then build on top of that (it is doing what they want, even if barely...)
Very risky. It would only make sense if that solution does exactly what the OP needs but lacks stability and some new features. However, it's very likely that the product is a generic one, and the OP will end up spending the next couple of years supporting features they don't need but are interconnected with the ones they actually use. This would be especially challenging if they buy only the rights/code without the development team behind it.
Maybe OP should approach the company and offer to buy it, rights/source code etc, then build on top of that (it is doing what they want, even if barely...)