Anyone who loses health insurance due to losing their employment (even if they voluntarily resign) is legally allowed to buy COBRA for 18 months. I think they are paying for it, otherwise this would be a fairly meaningless statement since the employer isn't involved with COBRA at all and that's less eligibility than any employee would have.
Something like that happened to me. I was a grad student until the project I was working on ran out of funding. Their website said if you left the program you could pay for health insurance out of pocket under the same plan you had while a student.
What they left out was that the company could reject you as a customer if you had a pre-existing condition. (This was before the ACA took effect.) They can legally do this because COBRA does not apply to grad students.
Fortunately, Oregon at the time had a state-subsidized health insurance plan called OMIP for people that were rejected by private health plans. The premiums weren't cheap, but they weren't worse than equivalent plans. Eventually OMIP was superceded by the ACA marketplace.
I worked for a company that was sold for scraps and they laid off all but there people. It didn’t affect me, I got a contract the next week with one of our clients that I worked with and paid for Cobra.
However, my Cobra eligibility died when the acquiring company cancelled their health care and moved everything to India.
