Well that is exactly what happened with my project and where my meager £14k was coming from. Incidentally, the thesis is just a document that only your examiners care about, all the important information it contains - i.e. your research - will get published in conferences papers and journal articles and these are what other research and industry are really interested in.

My project was sponsored by an interested industrial collaborator who kept a close eye on my work throughout the project. I don't know what percent of my salary came from their funding, but I suspect all of it did. The way it works (to the best of my knowledge) is the project's coordinator - i.e. my academic supervisor - will "win" grant money from a source interested in their research and that grant money is where the PhD student's wages comes from.

During my project a "technical collaborator" from my industrial sponsor would periodically visit us at university to overview how research was going (presumably to ensure their funding was worth it) and he would also provide his own technical thoughts on how the work could be improved. He wasn't a businessmen simply interested in profits, he was a scientist himself (also with a PhD) and it was in his interests that the research was as good as it could be.

You may be able to work directly at your industrial sponsor as a placement/internship if you can come to some agreement, where you can work for them for a few months and get paid a real wage during the time. I did this and it was very well worth it: I got good industry experience, I got a decent chunk of salary and I got some references and made contacts.