Depending on the company and country, they may or may not be able to do this. For example, I have been told (and IANAL) that in the U.S. if you ask to be laid off you don't get unemployment benefits.

Just start looking. "My company is having layoffs, I wasn't in the first one but it seems like things are not stable" is a perfectly acceptable reason to give your prospective new employer for wanting to move on, and it's always easier to interview when you aren't unemployed yet (easier to feel relaxed).