Some wavelet formats (SPIHT and EZW e.g) have the property that truncating the lossless version at 10% of the size gives you the 10:1 lossy rendering of that picture. That property holds not just for 10% but for any fraction of the file.

It's not quite the same thing, but a very highly compressed high-res picture would probably look okay in thumbnail format.

Some amount of data at the end of the file won't be usable, but it's easy to make a format that's resilient to you chopping anywhere.