Is this possible? Would bank be open to this idea?

I will try and explain this situation as clearly as possible. I know a real estate attorney would be who to call, but I'd like to know if anyone has ever heard of this before. I got the idea from Donald Trump listening to a Larry King episode, but I'm not sure this is exactly what he was referring to:

We are moving to another county in CA for work. We owe more than what our house is worth (owe $410, probably could sell for $350). The county where we are moving to is hit a little harder by the economy, is more rural, and there are a lot of foreclosures and REOs. Where our house is now is in a popular bay area county where it probably would sell relatively quickly at the $350 price.

Question: Would a bank/lender entertain the idea of switching their REO? If the bank is sitting on a REO at $350 and no prospects of it selling in near future, wouldn't they like to let us assume ownership of it, and they assume ownership of our house, which they could sell more quickly? It's a win-win. Bank has easier time recouping some of its losses, and we move into a house which would appraise higher than the house we are moving away from - even if we still kept the $410 mortgage.

make sense? I'm really hoping that this possibility exists out there, and that someone has heard of it.

Thanks!