If my temporary work ended.....
.....after over a year (in Ohio) and I'm filing unemployment~if the agency calls me back to return as a temp–will I lose my benefits if I don't?
Yes, most likely because they are your most recent employer and due to the nature of the work if you are collecting after the end of a temporary assignment .. it is a lack of work claim.
Turning down another assignment raises the issue of "refusal of work".
The suitability of the work can be an issue to argue that you had a right to turn down the work because it is "unsuitable".
I mean if you are some kind of office worker .. you wouldn't be expected to take a job you can't do .. but again, all states differ on the subject of what constitutes suitable work .. and when any work at all might become suitable, regardless of what it is .. because you are unemployed .. don't you know?
Since you live in OHIO .. that's the only state you need to be concerned with.I recommend you take a look at the Ohio unemployment legal abstract
I've moved your question to "Temporary work and unemployment". Temp agencies .. the new trend in American employment?
Now mind you, they don't make this stuff easy to find so scroll and click, scroll and click and don'[t forget to click on the links to the decisions when you find yor topic. IX: Suitable Work and even what's under VI.
Good Luck .. I mean it.