The Roman Catholic view seems to be that God created all the souls he would ever need at the Beginning, and installs them one at a time at the moment of conception. Protestants tend not to discuss this sort of subject. The RC Church has had a lot of monks and priests with a lot of spare time on their hands, so they have more documentation (actually speculation).
Babies are born without various appendages and arms all the time. But apparently, God never forgets to stick in the soul. Odds are in favor of a baby being born with none, but there are no records.
Spanish has a word "desalmado" which suggests someone born with a soul who had somehow lost it. It means cruel, a person without a conscience.
As for your question, I do not believe that the number of spirits in Tibetan Buddhism is limited. When a spirit attains nirvana, it becomes one with Brahma. Perhaps this causes a new spirit to appear.
When people do dumb things, they say that they have a "young spirit".
