A list field contains the comma separated sys_id's of the users and you are setting the entire field to 'empty', so that's just doing exactly what you explain it does.

Try something like this:

(function executeRule(current, previous /*null when async*/) {

        var userSysId = current.sys_id.toString();
        var cmdbCiGr = new GlideRecord('cmdb_ci');
        cmdbCiGr.addQuery('assigned_to', 'CONTAINS', userSysId);
        cmdbCiGr.query();
        
        while (cmdbCiGr.next()) {
            var assignedTo = cmdbCiGr.getValue('assigned_to');
            var assignedToArray = assignedTo.split(',');

            // Remove the inactive user's sys_id from the assigned_to list
            var index = assignedToArray.indexOf(userSysId);
            if (index > -1) {
                assignedToArray.splice(index, 1);
                cmdbCiGr.setValue('assigned_to', assignedToArray.join(','));
                cmdbCiGr.update();
            }
        }
    
})(current, previous);