If a specific person were named, I could see that possibly happening if said person were to ever set foot in the US (or maybe just Illinois).
But a company? That brings in additional questions. Would not Cook County have to prove that the person to be held in contempt had been employed by the company in question at the time of the subpoena? Wouldn't they also have to prove that responding to the subpoena would have part of said persons duties at said company? For example, if I were employed by EuropeCo in 2014 as an engineer on their Foomatic line of widgets, and travelled to the US next month for a conference, I don't think it should be possible for me to be held in contempt of court because someone didn't respond to a subpoena regarding EuropeCo's Baritron service. Yes, it's a silly and contrived example, but hopefully you get the idea.
I'm pretty sure Cook County would need to show some sort of nexus in order to compel, eg that significant business is done by the Romanian company in Cook County. Otherwise, anyone could break any laws so long as they didn't live in the place where they're breaking the law.
As is, providing an anonymous an non-specific service to anyone doesn't really satisfy that.
But a company? That brings in additional questions. Would not Cook County have to prove that the person to be held in contempt had been employed by the company in question at the time of the subpoena? Wouldn't they also have to prove that responding to the subpoena would have part of said persons duties at said company? For example, if I were employed by EuropeCo in 2014 as an engineer on their Foomatic line of widgets, and travelled to the US next month for a conference, I don't think it should be possible for me to be held in contempt of court because someone didn't respond to a subpoena regarding EuropeCo's Baritron service. Yes, it's a silly and contrived example, but hopefully you get the idea.
But again, IANAL.