That's a more believable attack than what most of the other posters have suggested. I suspect that the first step to fight that might be to store a value for the entropy of each backed-up file. A massive change in a file's entropy would be something to flag and require manual intervention on. Also, maybe some controls to limit the damage of a "push off the cliff by adding new data", like a way to set specific directories as "critical" to prevent the last copies of files in them from expiring.

I'm just playing with ideas =) The software I'm familiar with comes with hardware, generally scaled to keep a few months of nightly backups of a few hundred workstations and some fairly powerful rulesets for data expiration...so I've never really had to consider malicious backup expiration by ransomware. It's an interesting set of problems to consider.