With an object-oriented operating system, memory allocation and who is responsible for cleanup can get complicated. How does the BeOS handle this?

Of course, there are a couple of exceptions to this rule which we tried to avoid but found difficult. Those are specifically called out in The Be Book, the documentation of the BeOS:

http://www.be.com/documentation/be_book/

Finally, when a program exits, all of its resources are freed up by the kernel (open files are closed, memory freed, semaphores and ports deleted, etc.), though it is better when you do this yourself...