What happens if I approach and/or go over the 40,000 execution limit on the self hosted plan?
Self hosted Community Edition there is no enforced execution limit. You can run as many executions as your infrastructure supports.
In the Business and Enterprise, I think 
will be paused?
If you approach or exceed the 40,000 execution limit on the self‑hosted plan, your workflows won’t stop immediately. However, once you go past that limit, your executions may be paused or throttled depending on your configuration and the provider’s policy.
To avoid interruptions, it’s best to monitor your execution usage closely and consider upgrading your plan or optimizing your workflows before you reach the cap.