If someone might be eligible for unemployment but is also unable to continue working, should he apply for unemployment or SSI?

If he is eligible for unemployment and the amount is more than the Federal Benefit Rate (FBR)*, then he should take the higher amount (unemployment) as long as he can.  The medical approval for SSI will last for 12 months, so if the unemployment only lasts a few months, he can always reapply for SSI (the non-medical application) and SSA will use the medical decision from his last application. 

*This figure is updated annually and can be found at SSA Annual Updates.