If bitcoin precision is increased beyond 8 decimals, will the block reward continue halving forever instead of eventually going from 1 satoshi to 0 satoshi?
The "8 decimals limit" is not that, but rather bitcoins are a human readable representation for
100,000,000 satoshi: The software natively computes in satoshi.
What happens under the hood is that the limit of satoshi that a miner may claim by creating a block halves. Obviously, only whole satoshi can be claimed, (as currently they are indivisible), so after
block 6,930,000 when the reward limit drops from
1.164… satoshi to
0.582… satoshi per block, one cannot claim a whole satoshi anymore, as it would be greater than the limit.
If a new smallest unit of Bitcoin would have been introduced by then, we could continue to claim parts of a satoshi until the reward limit drops below that new unit.
In fact, we will be losing out on part of a satoshi in every block starting with
block 2,310,001 when the reward drops from
9,765,625 satoshi to
4,882,812.5 satoshi in approximately 2049.
There are several places where the 8 decimals property is listed as something that can change over time. This is true, but not in any meaningful way.
Of course Bitcoin can change. It's a piece of software that people run. If all those people agree to suddenly start using changed software, anything is possible.
Changing the number of decimals is not technically difficult. It would just require an extreme degree of consensus and coordination to make it happen. So unless not changing this is seen as a clear and inevitable danger to the Bitcoin ecosystem, it is very unlikely to ever happen (nor do I think it is necessary, but who knows what the future brings).
Once we decide to change the number of decimals, anything can be changed. Including, how the mining subsidy changes in the long term.
So, the answer to your question is: whatever the future Bitcoin ecosystem agrees upon.