Manual:$wgExtendedLoginCookieExpiration

Details
The purpose of this cookie is to allow having a different (usually longer, but this is not enforced) duration for "" login-related cookies.

This means you can e.g. set the standard cookie duration (widely used for MW cookies) to 30 days, but set the "" duration to a year.

The values mean: MW will follow  instead.
 * null -

"" sessions will last until the browser closes.
 * Positive integer - Duration of "" sessions, in seconds.
 * 0 -