The point of backups is that they still exist after something went wrong. Something went wrong, the backups didn't exist, DO didn't do the job it was paid for.
DO reserves say $20 (just an example) when one spins up a new droplet, and if one forgets to pay — then, DO shuts down the server. But keeps the backups, until the GB-month cost is $20.
One could choose how much money to reserve, depending on how important the data one stored on the droplet, was. If it's just for running test: $0. Customer data: Maybe $$$ instead.
There could be a default that made the data and backup last for 2 or 3 months?
And any remaining money would be refunded, if one closes one's account or sth like that.
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Actually I'll look into implementing this, in my own SaaS (which, like DO, takes monthly recurring payments and stores customer data).
I believe a solution like this is an elegant way to ensure that the customer gets what they 'believe' they are buying which is a sure-fire way to keep the customer happy.