hrrrmmm... of course I'm no American but wouldn't the employer portion of unemployment benefit contributions be the type of thing you pay DURING the employees tenure based on their hours/wage? Not after they apply for bennies?
This sounds hinkey. If you unwittingly didn't pay into it perhaps by them making their claim you are in for a world of hurt (or at least annoyance) due to the government now being aware of you being an employer.
From what I know of your business though I'm guessing you should tell these people they are sub contractors who have to deal with their own taxes/bennies/etc.
You'd better call someone (preferably a lawyer or accountant) to sort this out before phoning up the gov.
Again... I am totally not an American, nor an accountant and anytime I had people working under me it was as subcontractors or my superiors handled all that crap.
I would be VERY careful about what I did if I got something like that in the mail.
Good luck.