If Eurodollar never leaves U.S., then what do we mean by bring eurodollar on shore
Eurodollars can and do leave the US. They can be anywhere in the world: any bank outside the reach of the US Federal Reserve (henceforth "the Fed"). That's what makes them Eurodollars: they're US dollars in deposit accounts beyond the reach of the Fed.

That money is said to be "brought onshore" when it is transferred from a deposit account outside the reach of the Fed, into an account that is within reach of the Fed and its regulation / protection. This changes it from being a eurodollar to a dollar.

A US-based bank can have offshore banking subsidiaries and activities, and that's how it can hold eurodollars.

The whole point of a eurodollar is that it takes it outside the reach of the Fed.