I don't remember the specifics, but as I understand it, what the company pays for is a set amount of money based on your salary, into obra social. You can apply that amount towards private insurance (think of it as a discount toward private insurance), but you have to pay the difference between, for example, what Swiss Medical costs and what your employer covers from their contribution to your obra social. I've never had to deal with that either from an employer or employee side, but that's how it was exlpained to me some years ago when we were looking to set up a big shop here.
As far as I know, no business is required by law to pay into a private medical plan directly. It is up to you to apply to a private medical plan and make sure your obra social is paying that part of it to the private plan. It could be your employer originally handled all the paperwork and everything, but you needed to select Swiss Medical at some point, and surely you had to pay the difference. If you did not have to pay the difference, then possibly your employer agreed to pay that extra (and it would be more than your obra social amount) to be included as a part of your salary or something, but you were still paying it. Maybe you didn't understand that part?
But if the employer was paying your extra (i.e., over and above the obra social that they are required to pay) to Swiss Medical, I don't think they would be required to continue paying that extra portion after you were let go. While you have a right to continue to have obra social paid on your behalf by the employer because of law, Swiss Medical is not getting the rest of what they are owed monthly, because obra social won't come close to covering the rest of the payment. It's one of the most expensive private medical plans in Argentina, as far as I know. If you are not covering the extra between your 90 days obra socail and what Swiss Medical charges, Swiss Medical is not going to continue coverage. And your ex-company doesn't have to continue to pay that over-amount, unless you had that covered in a contract and it's not against a state contract that idemnifies the company from having to pay something like that.
Why do you think we often talk about the spread between public and private health care here so much?
I could be wrong, not understanding something, but it seems to me that's what your issue with Swiss Medical is.
And you are not without medical coverage, even if your obra social is not being paid (i.e., after your 90 days ends). That's what public hospitals are for. And that's what the majority of Argentinos and others who do not have the ability to afford private medical coverage, whether they are actually working in the white and covering it or not, have to deal with. According to many on the forum, public health care here is great. Of course, that's not my opinion, but you are far from not covered if you get hit by a car or something else befalls you.