In the USA, if some big and usually "non tech" company like McDonalds or T-Mobile wants to staff a whole project with programmers, they will usually have a relationship with someone like Infosys, Tata, Slalom, perhaps even Hitachi or Tech Mahindra or Accenture/Deloitte. These companies all pay you like a regular employee so you don't need your own drafted employment contract or business entity.

If you howver have a github/youtube channel/website where you make and release your own software, and someone contacts you saying "hello we want to pay you to add more features and or fix some problem for us", then you will need a contract and usually a business entity unless you don't mind being personally sued into the ground.

Such reachouts are very very rare unless your software has gone viral in the right circles, but I personally know at least 20 people who make a full time living this way. It seems pretty unenviable, and corporations whose email domain you would recognize routinely pull support or play egregious games with the definition of done. No cure for life, I guess :)