When you try to save such an image, the background area of the image will no longer be transparent and turns into solid color; in most cases, white i.e. Color 2.

Since the PNG already has a transparent background, you would just need to make it show up in Illustrator. This means you would have to enable the transparent background of Illustrator.

Making the background transparent – sometimes referred to as "punching out the background" by graphic artists – is a straightforward task in Adobe Photoshop.But depending upon the subject you ...