The equivalent in the startup space is a non-compete clause as a condition of employment. The contract typically identifies the consequences should there be a breach of contract (it could be a non-trivial fee or it could be millions). In the US, I've seen people that explicitly breach these terms without any consequences since many courts wouldn't uphold the terms and employees rarely have sizable assets that would make the lawsuit worthwhile.
That said, it is common for vendor/client contracts to include a clause forbidding the hiring of employees, and the vendor and client do have sizable assets to discourage a breach of this contract. I'd expect that any major sporting league would have an agreement with each of the teams in the league binding the owners to similar terms. If they breach those terms, the league may have the right to remove the team from the league or seek significant fines.
Therefore, it may be entirely possible for a player to quit working without notice and go work for some other company. However, no other team in the league would hire that person. They could still work as a coach for a high school or college, or any number of other jobs.
In the startup space, this isn't practical (try identifying every possible place your employee could go to work for next). Even in the few cases where these contracts would prevent one from hiring an employee of a vendor, I've seen employees go independent and operate through a middle man that isolates the client from any lawsuits. And really, no company wants to tarnish their image by trying to sue their employees, clients, or business partners.