The closest parallel to an equity structure would probably be to the employee-owned cooperative firms that exist in some jurisdictions. A crucial difference from startups is that equity is not tradable, not available to non-working investors, and cannot be taken with you if you leave the firm. Rather than owning securitized shares, you definitionally are entitled to a share of profits while working at the company; and everyone is entitled to the same share. So, for example, if there are 10,000 employees, you have a 1/10,000 claim on any dividends. If you leave the company, you no longer own shares. And there is no way to buy shares; cooperatives will generally only accept investment on bond or loan-like terms, not equity terms.
Sure, it's not as flexible, especially the totalitarian systems, though co-ops aren't as simply structured in their mature forms.
Look up "Mondragon" for what a modern form of distributist co-ops look like. Not the same share of profits, equity investment is the rule (limited to workers or co-op friendly orgs), and there are many other interesting aspects.
