A well barrier can include an annular seal element, an anti-extrusion backup having radially inward and radially outward portions, and a biasing device that exerts a biasing force against the radially outward portion of the anti-extrusion backup. A method of operating a well barrier can include setting the well barrier by decreasing a longitudinal distance between abutments of the well barrier, thereby compressing a seal element between the abutments, and unsetting the well barrier by increasing the longitudinal distance between the abutments and radially inwardly retracting an anti-extrusion backup positioned longitudinally between the seal element and one of the abutments. Another well barrier can include an annular seal element, an anti-extrusion backup, an abutment displaceable relative to the seal element to compress the seal element, a sleeve reciprocable relative to the abutment, and a biasing device that biases the sleeve toward the anti-extrusion backup.