Supplemantal Security Insurance(SSI) is means based so if you have the funds to travel internationally chances are you make too much for SSI. Social Security Disability Insurance(SSDI), on the other hand, is paid according to what you have paid in based on income and determined by whether you have been found unable to have gainful employment. SSDI can be collected while traveling, unless I am mistaken, but I don’t think I am. Maybe you have the two confused?