Supplemental Security Income (SSI) can and does count all other sources of income in determining SSI payments. The point of SSI is to supplement, add to, your other income.

Other income can include unemployment, SSDI, free food and shelter, inheritances, prizes, lottery or gambling winnings, gifts from family and friends, handouts, pensions, rental income, TANF, some insurance proceeds, income received by your spouse, etc.

So yes, SSI can and does and is supposed to use the amount of unemployment benefits you may have received in the past in determining how much your supplemental (SSI) check is. This will continue for as long as you are on SSI if you get any other income from anywhere. And since SSI gets information from the IRS, SSI can find out about pretty much any income you don't report. Then you end up overpaid.