This isn't the case even in EU, much less in US where they often don't sign any employment contract.
https://europa.eu/youreurope/business/human-resources/employ...
>When you hire staff, you should provide them with a written contract or an equivalent written statement confirming their working conditions
The fact it can be a statement rather than a contract may have an impact on the companies ability to change it at any given time without agreement from the employee, but I'm not an EU employment lawyer
When covid started, my company gave all employees annexes to reduce our pay by 20%, but keep our workload the same. I told 2 bosses, the HR employee and the director of HR mobbing me I will not sign and to piss off. I was the only one to do so out of ~150 employees. I kept my full salary until I quit my job because I don't like working for cunts.
In my country, which is in the EU, having someone work for you without a contract is a crime. Because by not having a contract you're denying them rights such as pension contribution, paid vacation, health insurance etc.
Plus you have to pay taxes on salary, so if you hire them "on a handshake" as it were, you're probably doing tax evasion too.