How to modify unity sprite border by script?

As far as I know you can't. However, you can recreate a sprite and then redefine its border using the Sprite.Create function. Once you have the new sprite you can replace the existing one.

For example if you have an existing sprite simply do something like:

 Vector4 newBorder = new Vector4 ( 2, 2, 2, 2);
 Rect rect = new Rect( 0,0, oldSprite.texture.width, oldSprite.texture.height);
 Sprite newSprite= Sprite.Create(oldSprite.texture, rect, new Vector2(0.5f,0.5f),  100, 1, SpriteMeshType.FullRect, newBorder );

Hopefully this helps you get closer to what you are trying to do.

newSprite.border.Set(x, y, z, w);

With AssetImporter it works. Got the idea (and main parts of the code) from https://answers.unity.com/questions/943797/editor-script-to-slice-sprites.html

In this example code it works by selecting one ore more sprites in the project window and executing the menu command below.

 [MenuItem("Tools/Textures/Modify Sprite Border")]
 public static void ModifySpriteBorder()
 {
         Sprite[] sprites = Selection.GetFiltered<Sprite>(SelectionMode.Deep);
         MoveTextureSprites(sprites[0].texture, sprites);
 }
 
 static void ModifyTextureSprites(Texture2D texture, Sprite[] sprites)
 {
         string path = AssetDatabase.GetAssetPath(texture);
         var importer = AssetImporter.GetAtPath(path) as TextureImporter;
 
         importer.textureType = TextureImporterType.Sprite;
         importer.spriteImportMode = SpriteImportMode.Multiple;
         importer.mipmapEnabled = false;
         importer.filterMode = FilterMode.Point;
         importer.spritePivot = Vector2.down;
         importer.textureCompression = TextureImporterCompression.Uncompressed;
 
         TextureImporterSettings textureSettings = new TextureImporterSettings();
         importer.ReadTextureSettings(textureSettings);
         textureSettings.spriteMeshType = SpriteMeshType.Tight;
         textureSettings.spriteExtrude = 0;
 
         string[] spriteNames = new string[sprites.Length];
         for (int i = 0; i < sprites.Length; i++)
                 spriteNames[i] = sprites[i].name;
 
         SpriteMetaData[] spritesheet = importer.spritesheet;
         for (int i=0; i<importer.spritesheet.Length; i++)
         {
                 SpriteMetaData data = importer.spritesheet[i];
 
                 if (!spriteNames.Contains(data.name))
                         continue;
 
                 // HERE MODIFY  data.border
                 spritesheet[i] = data;
         }
 
         importer.spritesheet = spritesheet;
 
         AssetDatabase.ImportAsset(path, ImportAssetOptions.ForceUpdate);
         return;
 }

Not sure, if the importer configuration part is needed.