I came across this question, where an industrial scientist wonders whether they'd have a chance to get into a PhD program in the US.

In my experience (Europe, biochemistry), they'd have a very large chance to get a position. You've already shown you can work, are productive, scientifically literate, and you might even bring some interesting industrial contacts. If you make a good impression someone might even create a job opening for you.

I understand that in the US you don't apply for a position with one professor, but you apply for a PhD program at an institute. You send a statement, recommendation letters, transcripts and GRE and hope for the best.

If I would be a professor in the US, what would be my options to hire such a person if they contact me? Would I have to convince a committee to let them in or do you usually have no influence? Could I just give them a position if I have funds available? I'm interested in the unofficial process in the US.

For a European perspective:

In my field, many positions are filled by hiring people that applied to a research group, even when there's no advertised or available PhD position. If there's funding available, professors check who applied in the previous months, and maybe put out a message to relevant research groups to get more candidates. People are almost always hired directly after completing their Master's, and they did one or two projects on a closely related topic.