On the other hand, what is fairly common is for companies to get saved out of bankruptcy by outside investment, in return for equity. This is a case of that with the oddity that it happened without contact between the company and the investors.
Interesting argument, but I think this is somewhat different.
A bankrupt company could always offer new equity to its existing creditors as part of a Chapter 11 reorganization plan, but that's not exactly a sale. If you're describing a transfer to outside investors, then the sale of new equity could violate fraudulent transfer law and the bankruptcy trustee could try to claw it back to preserve the value of the estate. (See Bankruptcy Code § 548).
It's worth mentioning that creditors can throw an insolvent company involuntarily into bankruptcy by petitioning the court. Since creditors don't share in the upside of a company (like equity holders do), there's no reason for the creditors to let the company linger in bankruptcy so that it can gamble for its resurrection. It's in their best interest for the company to enter bankruptcy as soon as possible so they can preserve its value and maximize their payouts.
There might be edge cases (e.g. if there's a single creditor who happens to have a significant equity stake, it could play out differently) but I don't think it's the norm.
Creditors may also share in the upside of the company if their bonds are currently way underwater, e.g. if your bonds are worth ten cents on the dollar you benefit from the company recovering all the way to 10x its value. Perhaps you should have forced it into bankruptcy earlier, but it's too late now. This isn't uncommon at all, as a poster upthread described "bonds in near-bankrupt companies trade like stocks".
In this case Hertz bonds trade around 40 cents on the dollar [0], so there's a significant incentive for the creditors to let the company gamble for some upside.
Yes and no. If a private equity firm injects a bunch of cash into a bankrupt company through an equity buy they do so with concessions, they might get one or two seats on the board of directors, a special clause in the bylaws in the event of a company sale or acquisition, etc. In this case these investors get none of that sort of 'armoring' of their risk.