Sounds like it could be a great find. :)
The 385 is a prefix that identifies the manufacturer. The numbers that follow the "385." contain the actual model number. (if the number is 385.550721, the model number will be 55, 550 or even 5507 - the logic behind the numbering is missing a few spokes)
Kenmores are usually very good machines and I think 385 indicates that it's Janome-made. (tho the memory cells don't fire the way they used to, so if someone else knows better, they can certainly correct that ;) )
Can't beat it for $15. :)