https://www.thenation.com/article/society/ssi-rules-families-poverty/
The Supplemental Security Income program (SSI) was created in 1972 under the Nixon administration to provide financial support to low-income seniors and disabled people. An effort to federalize state-level adult support programs across the country, SSI is a means-tested program—there are financial requirements to be eligible. In the case of SSI, as of its last adjustment in 1989, enrollees cannot have savings of more than $2,000 as an individual or $3,000 as a family. Furthermore, SSI beneficiaries are prohibited from having retirement accounts, life insurance policies, certain types of personal property, funeral/burial policies, and access to other types of income.
[emphasis mine]
OMG I'm gonna test some means! 
I didn't know that. I thought it only mattered if you were out of the country for 30 days or more. Here's what the FAQ says:
Excerpt
If you leave the United StatesLeaving the United States means leaving the 50 states, the District of Columbia, or the Northern Mariana Islands. Usually, if you leave the United States for 30 days or more, you can no longer get SSI.
If you move to Puerto Rico, you’re considered to be outside the United States for SSI purposes only. People who live in American Samoa, Guam, Puerto Rico, and the U.S. Virgin Islands cannot receive SSI.
If you plan to leave the United States, tell us before you leave. We need to know the date you plan to leave and the date you plan to come back. Then, we can tell you if your SSI will be affected.
After you have been outside the United States for 30 or more days in a row, your SSI can’t start again until you have been back in the country for at least 30 straight days. There are special rules for dependent children of military personnel who leave the United States. They may be able to get or apply for SSI while overseas. There are also exceptions for students studying abroad.
Source (warning: PDF). After what you've said, that "Then, we can tell you if your SSI will be affected" sounds especially ominous, but this page seems to indicate that benefits aren't affected if the time out of the country is less than thirty days.
Empire moment.
"Now sign up for our armed forces."
It honestly sounds like something they'd do, so I'll get a firm answer from a case worker beforehand if I ever have the chance to leave the country. At least I know for sure that although I can't leave my state for more than thirty days (given the state's portion of the benefits), they don't dock me when I'm elsewhere.