Unemployment and disability are two different things.
Unfortunately there are a lot of conservative voters on disability. Yet they complain about others leaching on the system. Disability payments is probably the most abused social welfare program and I feel like a lot of it is poor rural whites who vote republican.
It's a matter of pragmatism, something the right are more prone to. These people vote right because they want a system that makes it more viable to provide for themselves without assistance. Since they're not allowed to con gullible idiots with pyramid schemes, work outside health and safety regulations for efficiency or not pay taxes toward support programs, they game the system using the very thing they have a problem with.
Lefties are prone to idealism so are more likely to take the "go down with this ship" route if their ideology presents flaws.