Yes, its possible to have a modern piano with less than 88 keys.. some can be around 86, 82,, you may ever find some with even less, like 5 octaves.. but these are usually very old pianos. Its possible that someone may have gotten a hold of one of these old 19th century pianos, and refurbished it new.
but to find a modern (21st century) acoustic upright piano with a short compass (5-5 1/2 octave) would definitely be on the rare side of the spectrum,, I cannot even think of a maker.