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Odds?

You don't want to do that. Almost no offshore bank will touch US citizens because of FATCA and other trouble they ask for by doing so.
 
It depends on the bank and on who you are.

If you are worrying about FATCA, you are probably a US person. In that case, there is a near 100% certainty that the bank will report you, unless you bank with a non-FATCA bank in a non-FATCA jurisdiction. But even then, they may still inquire about Source of Funds.
But what if a u.s. legal resident somehow stumbled upon an offshore bank that didnt ask for source of funds and at the same time told them that they werent going to report them to fatca even if they knowingly knew ahead of time that they were only a greencard holder? What are we to make of this? What can we safely assume of such a situation...? They had like $100 million usd or more of undisclosed funds... would it matter at that point in what part of the world the bank/s would be located? Would the bank who told this potential client this information have great credibility? What would this say about such bank playing such a role...?
 
But what if a u.s. legal resident somehow stumbled upon an offshore bank that didnt ask for source of funds and at the same time told them that they werent going to report them to fatca even if they knowingly knew ahead of time that they were only a greencard holder?
You loose your money sooner or later and maybe also get prison for some time to think about how stupid this bank was.
 
But what if a u.s. legal resident somehow stumbled upon an offshore bank that didnt ask for source of funds and at the same time told them that they werent going to report them to fatca even if they knowingly knew ahead of time that they were only a greencard holder?
There are no such banks.

What are we to make of this?
That you're speaking with criminals.

What can we safely assume of such a situation...?
Anything is possible when you let your imagination run wild.

They had like $100 million usd or more of undisclosed funds... would it matter at that point in what part of the world the bank/s would be located?
You're either losing 30% of those 100 million USD (FATCA non-compliance penalty) or dealing with swindlers.

Would the bank who told this potential client this information have great credibility?
No, banks that violate FATCA and risk a 30% tax on all USD transactions and risk being cut off from having USD access would not have great credibility.

What would this say about such bank playing such a role...?
Most likely, that it doesn't exist.
 
told them that they werent going to report them to fatca even if they knowingly knew ahead of time that they were only a greencard holder?
I'd have to call BS on this.

1) Sketchy Bank (likely being surveilled already - guilty by association with the IRS CLI up your arse later on.
2) Risk taking bank which will result in Indictments in due course and a entrapment tool, IRS CLI up your arse sooner than later on.