Hi
A while ago I asked Ancestry about this. If you set your tree as PRIVATE no one can see it without they first ask you and then you allow them. My tree is private, I was asked by a family if he could view it, I allowed it, he promptly 'raped' my tree, added the info to his own and then set his as public, so all my work until that time is now public!!!
Very difficult to control any of this is my point here.
Now if we all kept our trees private we would never be able to share and learn. There are many articles /threads on here about that matter including one from me where I got fed up with people taking info from my tree (when it was public) and not telling /answering when I asked them how they are related - which is why i eventually set it to private in the first place.
So much information is available in the public domain it is EASY to track / find someone now a days anyway.
If you enter a person on Ancestry and do not enter a date of death then the Ancestry software will automatically calculate the 'age' of that person and if he /she is under 100 yrs of age that person will not be visible regardless of whether your tree is public or not.
But be careful, when entering people you must also check the appropriate box - living or dead - so it is even possible for someone born say in 1800 to be entered and shown as living i.e hidden, private- if you do not enter the initial data correctly and then the software takes over.
Hope this helps in some way