Kafka - Issue with multi-node cluster when some nodes go down

You would have to either not publishing with acks=ALL or you would need to insure your min.isr=1.

while it is possible, it is not recommended. Typically if your system is running with just 1 broker (there is no replication) and you can run into a data loss. If you have 4 brokers you could do replication factor of 4 with a min.isr=2 which would give you durability with the desired availability you want (handle 2 brokers being down).

Now, if you are going down the path of wanting the system to function with 1 broker, you have to make sure your __consumer_offsets topic is also configured to have a min.isr setting of 1 (as well as others such as the transaction topic if you are using exactly once semantics).