Retirement, Survivors and Disability Insurance (RSDI, the proper name for Social Security Disability Insurance) payments can NOT be paid to someone living overseas unless there is a treaty between that country and the US permitting such payments. Most countries have sign such treaties with the US, but I would check with SS before I move overseas.
Within the US RSDI payments stays the same anywhere in the US unlike Supplemental Security Income (SSI) which does change depending on how much the state you are living in supplements the Federal Grant of $579.00 per month.
For more on the Supplement see:
http://www.ssa.gov/pubs/statessi.htmlSome States SSI Payments (Both the Federal $579 plus the State's Supplement):
California: $812 (Federal $579, State $233)
Massachusetts: $707.82 (Federal $579, State $128.82)
New Jersey: $610.25 (Federal $579, State $31.25)
New York: 666.00 (Federal $579, State $87.00)
Rhodes Island: 636.35 (Federal $579, State $57.35)
Vermont: 631.04 (Federal $579, State $52.04)
States that pay a supplement as a separate Check from the Federal SSI payments (Pennsylvania, and I suspect other states, started this on January 1st, 2005 given the difference between what the Feds were charging Pa to add the State supplement to the federal SSI check AND what is cost the state to sent out a separate Check, The Feds were asking for something like $35 to add the $27.40 to the Fed Check and the State says it could do a mailing for 35 cents a check, thus the PA now sends out its SSI Supplement as a separate check or Direct Deposit):
Pennsylvania : $27.40 (Plus the Federal $579.00 equals $606.40)
For more states see (The information may be old so I am NOT copying here):
http://www.workworld.org/wwwebhelp/ssistatesuppfedad.htm