Indeed a limited liability company (LLC, or société à responsabilité limitée) may have only one shareholder (associé) at incorporation.

Also, neither the holding of all the shares of the LLC in the hands of a sole shareholder nor her or his death per se constitutes a cause for dissolution. 

References: Article 710-1(2) of the law of 10 August 1915 on commercial companies as amended; What is a limited liability company? December 3, 2020, Bertrand Mariaux.

*Podcast #316:

*YouTube Video 305|: 

Contributor: Cédric Buisine, Avocat

Editor: Hannah Seulgee Jung

Bertrand Mariaux, Avocat à la Cour, LL.M. (hons.)

Prestation de serment (Swearing-in oath): Luxembourg (2011), Certificat d’Aptitude à la Profession d’Avocat, École de Formation professionnelle des Barreaux de la Cour d’appel de Paris (2009), Bond University (LL.M. (distinct.), International Legal Practice, 2010), Université Sorbonne Paris Nord & University of Limerick (Master in European & International Law - major in economics, 2008), certified Expert in Microfinance (Frankfurt School of Finance & Management, 2015), social entrepreneurship (University of Oxford, 2015 & The Wharton School of Social Policy & Practice, 2014) and social & solidarity economy (International Labour Organization Academy - Social & Solidarity Economy, Organisation Internationale du Travail - Économie Sociale et Solidaire, 2017)