Re: So, what happens when bitcoins stop being produced?

Technically, Bitcoins will never stop being produced! Hooray!~

Are you sure about that? I thought that once the block reward is less than 0.00000001 BTC, there would be no further new bitcoin mined?

What if the precision has been increased by then? Could not the block reward then be 0.000000000000000001 BTC?

That would take a change to the protocol and there are no good reasons to continue providing a block reward at that point. It is not likely that a value of less than 1 satoshi will be significant for a very very long time. The value of BTC doubling at the same rate that the block reward halves (every 4 years) would mean a deflation rate of about 20%, which is not sustainable.