I see two things mixed together
1. a derivative system to stabilize value while someone else gets leverage, and
2. something akin to a fractional reserve banking system

I'm not sure how one ties into the other or why they must be connected.

Hyperbitcoins are leveraged and it is therefore possible for them to be underwater.  The owner can walk away, presumably losing their initial bitcoin 'collateral' but it is still a default.

If a hyperbitcoin were leveraged 2:1, say if it's effectively one bitcoin plus a derivative that's long bitcoins and short USD, then if bitcoins fall to below half their value, the hyperbitcoin is worth less than zero and the owner can discard it.  I don't see this as particularly unlikely since bitcoins today are less than half their high for the year.