The first time David Grupper was laid off from his job as an art director he was 58. It was 2013 and it took six months — and hundreds of résumés — to land another position as a manager of publications and marketing for the American Civil Liberties Union. A year later, he was laid off again.

Fed up, Mr. Grupper decided to try something new: being his own boss.

He teamed up with a friend, David Klein, to start a Brooklyn-based company, Point Made Animation, with $2,000 in savings. Today, they produce education and training videos for a dozen clients, including education technology companies and a consortium of community colleges in California. “The risks have paid off,” he said. “I’m making money doing what I love to do.”

The only drawback? He may never retire — and he has company.

A growing number of New Yorkers are starting businesses in their 50s and 60s, even as their colleagues are easing into retirement. They are crafting specialty foods like toffee — Oprah Winfrey is a fan — vegetarian dog treats and organic tempeh, a meat alternative traditionally made from soy beans.

One former executive at Lehman Brothers, who lost a chunk of her retirement savings when the firm collapsed, has since parlayed her corporate skills and experience into a recruiting service for financial and real estate companies. A speech therapist whose job was eliminated decided to help immigrants communicate better.