Save the files in a folder inside the application support service. They will be saved, and iOS will not delete them. I say that I use a folder, since later, if you want to delete them, you can simply delete the folder.
Exactly how to access and configure the application support directory in detail in this post
If you want, you can save the URLs or paths to these images in the Core Data repository.
EDIT: I have a singleton class that manages my Core Data image store. An object that has an image associated with it has a data property, a URL property, a filePath property, and a boolean flag indicating whether there is an outstanding selection. When something is needed for an image, it requests an image (which is created from the data), and if there is no data, then singleton issues a web selection for it. When it arrives, it will be saved in the file system, and the entity will receive filePath for this set of images. He then sends a notification that such and such an image has arrived. [For debugging, at various points I also checked so that I could create an image from the data.]
When viewControllers receive a notification, they look at a list of visible cells, and if any of them is associated with a recently received image, this class requests an image from a singleton and then sets it to a cell. This works for me well.
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