"I'll be resigning when [the board/leadership] finds a replacement."
I always get massive push back when I suggest this, but it's the only remedy that makes sense. If you have to layoff 15% of the workforce when the growth was under your command, and you want to take responsibility, then step down. Own your mistake.
For startups such a step is likely to ruin the company. And in any case that founder would keep their stake in the company while not being able to influence it anymore. Doesn‘t make sense.
That's only true if the company is better-suited to be run by someone else. CEOs are prominent, but they're still just people. A person can make mistakes and still be the best person for the job.
What if the board doesn't want you to quit? Surely it's better to do what's best for the company going forward rather than to broadcast your self-flagellation.
The goal of the business isn't to maximize employment. It's to maximize profits. Getting rid of employees doesn't mean the CEO did a bad job of maximizing profits.