I see your point. The underlying assets of a stable value fund are the the bonds that the fund owns. I may be missing a few subtleties in how they work, but basically the wrapper agreement allows investors to buy and sell their holdings in the stable value fund at the par value of the bonds, rather than at the bonds' current market value. As a result, stable value funds in normal times behave similarly to money market funds, but with bond-like yields.
If the insurance company behind the wrapper agreement were to go bankrupt, the stable value fund would still own the bonds that are the underlying assets of the fund, but would no longer be able to pay redemption requests at par. Instead they would have to sell the bonds on the open market and so the asset value of the stable value fund would fluctuate in the same way as a bond fund.
Here is an excerpt from the prospectus of my own stable value fund regarding investment contract risk.
To me the take away from all of this legalese is that stable value funds are relatively safe, but do not have the same level of security as an FDIC insured bank account or treasury bill. I looked into the risks of my stable value fund several years ago and decided to continue using it for most of my fixed income investing, but to also have a generous share of regular bond funds in my portfolio, so as to not put all of my eggs in one basket.