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 should be $5077 for an individual or $7516 for a family today if adjusted for inflation.
Which is still pathetic obviously, there should be no limit or if you really feel the need to have a limit it should be like, $100k or more, but $5000 would still be such a huge improvement