I am thinking if there could be an easy way to guarantee eventual consistency in an event driven modular monolith, which is utilising an in process message bus instead of an actual external message broker.
All solutions out there seem to utilise message brokers with transactional outbox pattern to guarantee the delivery of the domain events to the message broker. On the other hand there are examples of modular monoliths which use the mediator pattern (in memory message bus) for the domain events communication. It seems that there is no trivial solution for making the modular monolith eventually consistent in this case.
What could be the possible solutions for this problem if we do not use event sourcing? Any propositions?
A common approache is to use your DB as a queue, so just having an "outbox" is (or queue table) enough. You then have one or more threads that read from that table as if they would be reading from a broker. For example, in postgres, this can be implemented using 'SKIP LOCKED'.
Please check this project to have an idea of how it works: https://github.com/ecodia/simple-postgres-queue (I'm not the author of that project, and I'm just pointing at it for inspiration).
Depending on the load, you can implement the same on any database.