When checking out ETFs, I had this same question. This is what I found:
http://www.etf.com/sections/features/5461-structural-risks-in-etfs.html?iu=1&nopaging=1That particular discussion covers more scenarios than you describe, such as the failure of the ETF sponsor, the failure of the insurance carrier, the failure of the custodial bank holding the assets, and the impact of those failures on various types of ETF organizational structures and types.
Bottom line is that different laws apply depending upon the circumstance. In general, you might be inconvenienced, or you might not have access to your money for a while. The worst case is that you would lose your money, but the most likely worst case is that the ETF would be liquidated and your money returned to you (you may then be subject to capital gains or losses). The most likely result would be that a new investment company would take over and either buy the failed company or their assets (particularly if it was a popular, well-covered ETF), and there would be no change.
I don't see why the FED would step in. That's not what they do. ETFs are not covered by SIPC insurance (they're not a brokerage). They're regulated by the SEC, but this does not extend to a bail-out.