Monero has a tail emission designed to protect against lack of incentives to secure the network.
Here is an excerpt from a good post explaining the reasoning for this:
It at this point where we see the critical importance of a tail emission since if Rbase = 0 this attack has zero cost and the tragedy of the commons actually occurs. This is the critical difference between those Cryptonote coins that have a tail emission, and have solved the problem, such as Monero and those that do not, and will in a matter of time become vulnerable, such as Bytecoin.
[2] Initial number of atomic units is M = 2
64 - 1. However, once the block reward reaches 0.3 XMR (sometime in 2022) that is treated as the minimum subsidy, which means that Monero's total emission will forever increase by ~157783.68 XMR annually.
[3] Uses a recurrence relation. Block reward = (M - A) * 2
-20 * 10
-12, where A = current circulation. Roughly 86% mined in 4 years (see
graph).
At the time of the Monero hard fork in March (when they will switch from 60 second blocks to 120 second blocks like Boolberry has now) the tail emission schedule will be adjusted accordingly.
Aeon also appears to have plans to include a tail emission:
Okay let's consider this an official proposal then, open for comments:
Once the base reward declines below 0.3/minute, then reward will switch to inflationary at a target rate of 0.8888888....%/year (actual rate may deviate slightly in practice due to variations in block rate, block reward penalty, rounding, etc.)
This is what the Monero tail emission will look like (offering continued incentives for miners to protect the network in addition to transaction fees).

Boolberry could implement something very similar although it will take us twice as long to reach the "tail" due to our slower emission schedule.