Regions can be saved inside TIFF files. Whenever you save a bitmap containing a region as a TIFF file format, the region is also saved.
When you save a bitmap with a region as a CUR or ICO file, the pixels inside the region are considered to belong to the icon/cursor data. The pixels outside the region are considered transparent. If you save a bitmap without a region as a CUR or ICO file, the whole bitmap will be considered icon/cursor data. In this case, you will get a square icon or cursor.
If you save a bitmap with a region as any other file format, the region will be lost. If you want to preserve the region, you can:
Save it to a 1-bit mask using the LBitmapRgn::CreateMaskFromBitmapRgn function and save the mask as a separate file. When you load the bitmap, you should load the mask bitmap and set the region using the LBitmapRgn::SetRgnFromMask function.
Save it to the alpha information in a 16/32-bit image. You would convert the region to a 1-bit mask using the LBitmapRgn::CreateMaskFromBitmapRgn function, after which you would set the mask to the alpha channel using the LBitmapBase::SetAlpha function. During load, you would get the alpha bitmap with the LBitmapBase::CreateAlphaBitmap function, convert it to 1-bit if necessary and then set the region with the LBitmapRgn::SetRgnFromMask function.
NOTE: To save a region inside a TIFF file, you must have an unlocked Document, Vector, or Medical Imaging license.