It is hard to imagine why it would "go away". It is a valuable asset, and even if the owner of the deficiency claim were to go out of business or into bankruptcy, the receivable would be sold. There are lots of buyers for these things, primarily debt buyers.
As for negotiating it down, unless you develop some meaningful leverage, it is not likely to be reduced much. Once reduced to judgment, the claim has a potential life of 20 years.
Bankruptcy is the only CERTAIN answer. However, at such time as the deficiency claim is made, the claim may turn out to be legally defensible, and if you wage a good defense, you then develop some negotiating power.
I am defending several deficiency claims currently, and am finding numerous defenses. I have won two completely. However, there is no way to say today what defensive opportunities (if any) may present themselves when suit is filed, so that would have to be a "wait and see". The challenge is that there is a 5 year statute of limitations on making the claim, and so lots of time yet for the owner of the deficiency claim. If you are a good candidate for bankruptcy now, but don't file, and then 3 years from now the claim is made, you may no longer have a favorable bankruptcy profile, and therefore the bankruptcy option may no longer be there.
In addition, even if the creditor were to forgive the deficiency (not that I expect that would ever happen), you would be taxed on the entire amount forgiven as income, and then would owe lots of taxes on the $300 shortage. If you discharge the debt in bankruptcy, that problem should not affect you.
I would suggest you at least speak to a good bankruptcy attorney now, to get a sense of how your current situation would look in bankruptcy. Bankruptcy can be a miraculous solution.
Please note that the above is not intended as legal advice, it is for educational purposes only. No attorney-client relationship is created or is intended to be created hereby. You should contact a local attorney to discuss and to obtain legal advice.
It all depends on your disposable income and what assets you want to keep. From what I've read though, it looks like Chapter 7 works fine for you.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here. Please visit my web site: www.avanesianlaw.com for more information about my services.