They should not ask for your I-20, or anything else for that matter.
Turning in the I-94 should be enough.
However, to be fully compliant with the laws, you would have to inform
all authorities that you no longer reside in the US. This would most
likely mean informing the Dept. of Motor Vehicles (or whatever it's
called in your state) and giving up your Driver's License. You may want
to ask about possible tax implications, if you don't do this. IRS may
consider your residence in the US to be continued and require you to
declare your worldwide income for tax purposes, unless you notify
everyone of your change of address.
The above is mostly guesswork on my behalf, I just meant to point you
in the (right?) direction, so that you don't miss anything.
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