I could also get into a the whole definition of executory contracts and the effect of discharge, but that is a whole other post.
My final thoughts are this:
Agreements/contracts/promises are all just a person's word that they will do something. I loan you $100 and you promise to pay it back...
When you fulfill your promise (by paying me back), you have discharged your obligation (hence why a succesful bankrupty is called a discharge- it ends your obligation). As long as your promise is not discharged, than it is executory. At any time an executory contract remains unfulfilled, the promisee can try to make the promisor fulfill the promise. An executory promise within the SOL has a special attribute called "enforceable."
As long as an executory promise remains enforceable, the government will help a person enforce the promise. After the SOL, the government basically says "you can try to recover your promise but we're not going to help you anymore, you're on your own; it's wasting our time to go further." And thus the promise is still executory but is now "unenforceble".
The SOL is just like an on/off switch, as to whether to courts will help you or not.