COMEA saved COME APK and an offline phone
A completed APK can exist on a phone without an active connection. That does not mean the app's account or online features will work offline.
Check that the file finished
A browser entry marked completed is different from an interrupted partial file. Inspect the saved item and its source before opening it. A file's presence alone does not prove that every byte arrived successfully or that the file is trustworthy.
Read Android's response
Android may be able to process a local installer, but device checks or later app functions may still depend on connectivity. Follow the actual prompt. Do not disable protection or assume an offline state avoids normal installation checks.
Separate later failures
If installation finishes but the first app screen reports a network problem, downloading another APK may not help. Restore a usable connection and revisit that screen. Account recovery, messages and service content can require their own online requests.
A useful next step
Identify whether the unfinished task is file transfer, installation or connecting the opened app.
Related: COME download help: installer error or network error?