Don't trust it to chance or broad statistical measures. Figure out the sustainable organization's size and mission. Then do the layoff, and do your best to recruit the rest to stay with you to fulfill the new mission.
Attrition after a layoff depends on a lot of things out of a company's control. As you mentioned, if the company is doing badly and the surrounding economy is doing well, people will act in their self-interest and leave when they can.
If people like the ones you laid off are relatively easy to recruit and train, you probably measure attrition as turnover (the percentage of employees leaving in a time period). Your question might be "do companies have extra turnover after a layoff?"
If you have a professional staff where salary cost needs to be reduced, "across-the-board" layoffs that hit each department proportionally are a terrible way to proceed. It looks exclusively backward at the business's problems, and not forward to a new plan. The only reason for planning that kind of layoff is a fake kind of "fairness" that demands that the pain be distributed equally. If this happens, probably the company's line managers are fighting to blame each other and "across-the-board" is the compromise.
If this is happening, the savvy non-management employees know it. I've seen it happen. The most savvy employees get disgruntled and quit, leaving the rest.
I worked once at a 40-person company where the personnel manager used to read names on the public address system on Friday afternoons when business was slow. "Joe, Jane, Bill, Tom, please come to the personnel office." Everybody knew to say goodbye to them on their way to the front office. This was TERRIBLE for business. Several times we had other, highly valued, co-workers simply abandon their jobs and not show up the next Monday. I don't know about turnover statistics, but I do know that quality decreased sharply when the good folks walked away. That made business get even worse.
What's a better approach? Figure out how to refocus the business, then how to explain it, then do the layoff.
If you have a few troublesome people, get rid of them. In the US, we have "employment at will." Lay them off. Just do it. If you lay them off and don't oppose their attempts to collect unemployment insurance, you'll probably be OK. The rest of your crew will thank you.
If a new contract signing is delayed, tell the truth about that. Furlough the people who would have worked on it.
If revenue from an old product line is decreasing, what are you going to do about it? "You can tell them, 'we're discontinuing the zumbinatrons and outsourcing support to our number one dealer, because we aren't selling as many as we used to. Unfortunately that means we let two sales people, three support people, and two engineers go. The other people from that team are now working on the luxatron line, which has a bright future according to our dealer network.
See how this goes? Figure out what the future holds, figure out who can do what in the future, and lay off the ones who don't fit as well as the others.
In my limited experience, one in ten will file a discrimination complaint, justified or not. This risk can be mitigated by doing a good job with severance packages and documentation.
