The French government has owed Marie Verrier’s family money for a long time. Almost 300 years.

All Verrier and her husband, Jean, have to do to claim the world’s oldest government debt is prove they are the descendants of an obscure 18th-century lawyer.

“ ‘That [yield] would allow you to buy a baguette of bread once a year.’ ” — 81-year-old Marie Verrier, speaking from the couple’s home in the Parisian suburb of Asnières-sur-Seine

The question is whether it’s worth the effort: Three centuries of inflation and shifting currencies mean this debt yields just €1.20 a year, the modern-day equivalent of the long-defunct livres the bond was issued in.

Bonds that never mature, or do so after a century or longer, aren’t just museum pieces. The ultralow interest rates of the last decade have encouraged governments and corporations to borrow for increasingly long periods, with some even selling 100-year bonds now.

Argentina, Mexico, Oxford University and the Wellcome Trust, one of Britain’s largest charities, have been among the issuers bonds that will mature in a century. Countries including Japan and Germany have issued so-called perpetual bonds, which never mature.

An expanded version of this report appears on WSJ.com.

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