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! 
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.