Access previous build artifacts in new build?

During the build process is it possible to access artifacts built during the previous build? I am using an API which isn’t very reliable and if the call to it fails I would like to use the response I got from it during the previous build. Is that possible?

Could you call the API via a function which returns an error until you achieve the desired output, like #6 here?

What’s the API actually doing, is its output used within the build? Do you have a link to a deploy or additional context?