Yes. Employers allow people to opt out (for example, their spouse has a better plan from their employer.) Some employers will actually pay a small amount of the money that is paid for insurance to you if you opt out (i.e. to encourage people to go with the spouse's plan and save the company money.)
I have never heard of any company paying employees the FULL amount that would be paid for insurance if the employee opts out. Even if they did, the money would be taxed at your marginal rate, leaving MUCH less money to buy insurance in the market.
Is it technically feasible to get insurance apart from your employer when you have a salary/benefits job - Yes. Is it practical - Not really.
At the last job I had which offered insurance, the only way anything was taken out was if I chose to enroll in the insurance program. Prior to enrollment I paid nothing into the pot. Perhaps it was an isolated case? I worked for a university, though I’m not sure that’s relevant.
I have found that the plans I could have gotten via the above link were much more affordable and equally beneficial as what I had via the university.