Have you been noticing more “spam” in your diet lately? I’m not referring to the luncheon meat, of course, but to unsolicited messages that may arrive in the form of emails, text messages or—increasingly—phone calls.

Spam calls may have received a boost recently thanks to the partial government shutdown. Among the casualties of the shutdown have been the Federal Trade Commission’s “do not call” registry and the Federal Communications Commission’s online complaint system. Both services are designed to tamp down the “robocalls”...