1. If it's "heir"--not just descendant but the one heir--the firstborn, then one who is orphaned, assuming no living grandparent that was the heir, then there would be just the one.

2. Or, if it means heir in the sense I've thought it did, which meant, also born of that line with the gift/talent of being a Parselmouth, then there might be only one, as it's stated to be rare.