The Oort limit is a theoretical location at the outer limits of the Oort cloud, where the amount of comets and minor planets orbiting the Sun drops drastically, or drops entirely.
The exact location of such a limit, if there is such one, is uncertain.
So far, it appears that rather than a sudden drop in the amount of comets orbiting the sun at about 50,000 AU, the Oort cloud rather uniformly decreases in size, the further away from the Sun it goes.
As current observations indicate, the Oort limit is somewhere around 50,000 AU (0.8 LY) from the Sun.
Considering this, Oort Cloud comets are fairly common.