ReBuzz Backup and Restore copies your whole site, every file and the entire database, into a single archive you can download, move, or restore later.
Most backup plugins assume the server will let them finish. On shared hosting it often won’t: PHP gets cut off after thirty seconds, memory caps out well below what a large site needs, and a half-written backup is worse than no backup at all. This plugin is built the other way round. Nothing it does happens in one long request. File scanning, zipping, the database export and import, extraction, URL rewriting, all of it runs in small batches that pick up where the last one stopped.
wp-content/uploads/rebuzz-backup-and-restore/backups/ over FTP. It turns up in the restore list on its own, with no size ceiling.