The requirement to be actively searching for work has actually been temporarily paused in many states, including eg/ CA https://www.edd.ca.gov/unemployment/eligibility.htm. Presumably that provision will be removed along with the SIPs, but just figured it was worth being precise here.

That seems to rely on an assumption that there's no variation in amount or quality of job searching effort, above the minimum required, which might be influenced. It also assumes inability to fake a job search, or sabotage an otherwise legitimate one, which might let an individual so intending to fall below the required minimum. The latter seems questionable, the first seems wrong.

The CARES Act extends unemployment benefits through the end of 2020 delegates to the states what the job search requirement means. States have a strong incentive to interpret it loosely because the federal government is footing the bill. Additionally, the “offered employment” thing is not hard and fast line. Restrictions will be lifted incrementally—there will be no “everyone back to work moment.” Businesses with furloughed employees will want to call them back up sooner rather than later, but workers earning more on unemployment have an incentive to not come back to work as soon as they could. Businesses, particularly smaller ones, aren’t going to be in a position to say “come back or you’re fired.” (Can you imagine the liability?) It’s during that transition period when the incentives could slow down the recovery.