Financier works by syncing your transactions up to your trial expiring, and after that, your data no longer syncs. The idea is that your can use Financier like the free version after that, but if you lose the data locally on your computer, you will only be able to recover data right up to your subscription ending.
Unfortunately, unless you created a backup to your computer, your data will not be recoverable.
I'm really sorry that you lost your data after your subscription expired, I realize how frustrating that must be. Even though your subscription ended, I could probably do more to make it more apparent that your subscription has expired.
Chrome (and other browsers) don't guarantee that data won't be deleted at any time (they do it when space is becoming low on the computer, among other undocumented reasons). Which is why it's so important to have a sync mechanism like Financier and/or create local backups of your budget every now and then.
For anyone else -- You will get an email when your subscription expires, and you will also notice that it says "Subscription expired" where it used to say "Syncing" or whatnot.