Yes. It is possible to receive both unemployment benefits and SSDI or SSI, but it gets tricky.

Generally, when you apply for unemployment benefits, you attest that you are ABLE to work but you lost your job through no fault of your own and are actively looking for work. When you apply for disability benefits, you attest that you are UNABLE to work at a substantial gainful level.  Some judges see this inconsistent, others don't seem to care. I've seen both situations.

During the Coronavirus epidemic, the government suspended the looking for work requirement, opening up several arguments that simply collecting COVID unemployment benefits should not stop you from qualifying for disability-based benefits.

If you collected COVID unemployment and are now seeking disability benefits, SSD or SSI, you need a competent attorney to maximize your chances of winning.