At around 3 p.m. on Nov. 23, Paul Deutsch was working at DePaul Lettering, the print and embroidery shop he owns in the suburbs of St. Paul, Minn., when he got a surprising phone call.

It was Bob Mason, the goaltending coach for Deutsch's hometown NHL team, the Minnesota Wild. Mason told Deutsch the Wild was in a fix: One of the team's two goaltenders, Niklas Backstrom, couldn't play that night against the Nashville Predators because of personal reasons.

The...