It is possible to sell with a huge debt on a property and it was one of the things that Cenk and I highlighted when people came up with the old "cut out the agent, go direct to the builder and save the 3%" - mind you, those people generally didn't listen and saved the 3%. Some subsequently lost their property but hey, 3% is 3%.
So how does it work...
1. Buyers go direct to developer (to save 3% wasted paying estate agent)
2. Contracts are agreed and builder takes power of attorney for purchaser to save them having to come over all the time
3. Builder takes out huge loan secured on the property he just sold, prior to changing ownership to purchaser's names
4. At deed office, deed man says "It is my duty to inform you that there is a humungous fecking debt secured on the property you are about to sign for on behalf of those British people.
5. Builder says "Yeah I know, it was me who got the loan - where do I sign the property out of my ownership and my life"
6. The property, and loan, transfer into the ownership and responsibility of the purchasers
So there you have it. If you buy through an independent agent this is pretty much impossible.
By the same token, if you didn't go direct to the builder without an agent - and give the builder PoA, you should be fine.