To add to the other answers: It is a good idea to create a paper contract (possibly even with a lawyer present) with the other party to clarify that the person who signed the contract with the rental company will be reimbursed by the non-signee for any monetary costs following from an action or inaction from the non-signee while he is using using the car.

However, The rental car company won’t allow you to coregister a driver in absentia, because any respectable rental company will demand to see the original driver’s license and ID of all drivers you register. For example, EuropCar states this in their FAQ:

Question: What documents do I need to present at the Europcar counter
when I pick up my car?

Answer:

You will need to present to our customer representative:

1) your normal driver’s license, issued by your country of residence
and held for a minimum period according to local legislation or
conditions. It will be requested at every rental. In addition to your
normal Driving Licence, your International Driving Licence is also
mandatory if your driving licence is written in a language different
to the one of the renting country and/or in characters that can not be
read in the renting country. Note that your International Driving
Licence is valid only if accompanied by your normal Driving Licence.
Driving Licences must be valid in the country of rental.

2) your identification document such as your passport (or your
national identity card) may also be required for some destinations and
/ or a utility bill issued less than 3 months ago and showing the same
address as on the utility bill. Within the countries of the European
Union, identification documents are generally not requested from
drivers resident in the European Union, except in some specific cases,
such as certain special or luxury vehicles.

3) your valid credit card with an expiry date after the due check-in
date or a valid Europcar charge card. If you use a Europcar prepaid
voucher as means of payment (with a specified value or the mention
‘Group & Days apply’), you must also present a credit card for those
charges which have not been prepaid (such as extras, refuelling
charge, excess due in the event of damage to or loss of the rented
vehicle). Please check the list of accepted credit cards in the
country rental conditions.

NOTE: Points 1) and 2) are applicable to all additional drivers, if
any

Hertz states this:

Do Hertz allow additional drivers?

Yes, you may add one or more additional drivers to your rental. This
cannot be done online. It can only be done at the time of pickup of
the car. All intended drivers (main and additional) must be present at
the time of pickup and show their driver’s licenses.

Regarding the Risks

Yes I think it could be possible for you to find someone willing to drive your car back. As MarkMayo suggested there are a few options out there including organised services, as well as other travellers’ forums (LonelyPlanet, etc).
In the case of an organised service such as Transfercar I would assume they have all the legalese figured out for you. However, in the case of a more social globetrotter-to-globetrotter organisatio, the question is would you trust a complete stranger to return a vehicle you rented? I would consider the safety and economical risks this involves.

Speeding and Other Tickets

First and foremost as MarkMayo again duly pointed out is the fact that the car would be registered in your name, so you might end up getting road tickets without you being the driver.

Authorised Drivers

More importantly though is the fact that being you the only registered driver only you would be legally allowed to drive the car. This is true both from an insurance point of view (very important), as well as a criminal point of view (very very important). Imagine how much you’d have to pay if the return driver crashed the car. Even worse, imagine the return driver being stopped by the Police for routine controls. I think the Police would immediately assume the car to be stolen, and they would be right to do so.

Of course I agree that your fellow globetrotters would have no interest in wrecking the car or driving through all the red lights in America. However the situations I mentioned are the classical unexpected glitches that never happen but when they do someone ends in big trouble.

Bottom Line

So the bottom line is that the safety of such a procedure depends on the legal small print of the rental contract you sign.

Workarounds

Registering Drivers In Absentia

I know that Hertz/Europcar and others require you to register all authorised drivers for insurance purposes. I never tried registering a driver that was not physically there with me when signing the contract. It might be possible though. You could call and ask. This would solve the insurance and police control problem. It would not however guarantee that you don’t end up paying for someone else’s speeding ticket, as I believe the fine would be addressed to the person signing the contract.

Sort of. It’s simpler than that, and potentially far cheaper. You just need to be flexible. Services like Transfercar allow you to return cars for free, essentially.

The idea is that generally more people travel in a particular direction when renting – the flow is not even. In New Zealand, for example, many renters get a car in Auckland (most common arrival), drive south, and then fly back to Auckland (or even out of Christchurch) instead of driving back the same way they’ve come.

As a result, you get a bunch of cars ending up in the wrong place. So services like this essentially pay your gas and give you a period of time to return the car to the original point. Saves them major cost, and you benefit greatly.

So maybe it’s not quite what you were thinking of – although you could look at something like Lonely Planet’s forums if you really wanted to try and organise that, but you’d have to have two drivers registered, sort insurance and other complications. Plus you might get pinged for their speeding tickets, etc.

If it’s possible to work it to your schedule, this would be a workable solution, I believe.