Ask HN: Life cycle of a company?

So let's stay I start a startup, grow and manage to take it public, what happens next? Is the company expected to keep growing indefinitely? What happens if growth is stagnant, but the company is profitable?

I also hear about the mid-life and late stage of companies. Can you explain what these terms mean and how being in these stages affects the company?

Are there any good examples of publicly traded companies which have lasted a long time (more than a few decades) with minimal impact of the "we have to keep growing" mindset?

Finally, what are the pros and cons of being private without vc funding and being a public company?