How does the Stop Processing Rules action work in Engagement Engine?
In an Engagement Engine rule, you can add the action Events: Processing Rules > Stop Processing Rules for..
All Site Rules
When selecting the option to stop processing rules for all site rules, then none of the next rules will execute after this rule.
Note that the current behavior is that all rules are being triggered at the same time, so this configuration requires to add a "Timeout" condition of at least 1 second for all the rules which should be met after the "stop processing" rule, in order for this action to work. Otherwise, all rules will continue to run, regardless of the Stop Processing rule. See this documentation page for additional details: Timeout.
Once the page is refreshed, it will trigger a new evaluation for all rules.
Current Rule
When selecting the option to stop processing rules for the current rule, then the same rule will not execute again. Note that this action is relevant only when you choose to evaluate the same rule multiple times, and stopping the current rule may act as an exit to that. See this documentation page for additional details: How Rule Evaluation and Rule Execution Work