If Eurodollar never leaves U.S., then what do we mean by bring eurodollar on shore We already know that Eurodollar never leaves U.S. But then what do the media mean when they say bringing U.S. dollar offshore (eurodollar) onshore? Isn't it always onshore? (Let us omit the real physical cash)

Also, the Fed website says that both Eurodollar and Fed funds liability do not have reserve requirement. My question is how can banks in the U.S. hold eurodollar liability? I mean, eurodollar is defined to be U.S. dollar deposited off-shore or IBF. So doesn't that mean U.S. based banks cannot have Eurodollars by definitions? And since eurodollar does not leave the U.S., its borrowing in Eurodollar market in its off-shore branch is actually simply a transfer of Fed reserve from the lender's bank's U.S. bank to the borrower who is a U.S. based bank. Then the liability of the U.S. based borrower shows up as time deposit due to its off-shore branch. So I think this is how banks borrow from Eurodollars market. But the above question remain.

Any comment is appreciated.

http://libertystreeteconomics.newyorkfed.org/2015/05/the-eurodollar-market-in-the-united-states.html#.VjvTKIQt82Z
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.