I bought half a stamp once.
It was from an auction house where people that cut up multiples off-load the scrap. This was the only time I ever bought there - but in all fairness, even the auctioneer was surprised that I was bidding on it, and he made sure that I understood that it was 1/2 of a stamp.
It was a US #7 1c Ty II - or about 1/2 of one - cut off at the top vertically. But from the bottom label, it just seemed as though it had to be a plate 3 (a scarce plate I was trying to reconstruct).
Naturally I was never able to plate it (seeing as 1/2 of it was missing!!) and it sat in my album for years just really making that page look bad.
My new stance is never buy less than 2/3'rds of a stamp now.
