Hello Ricardo,
yes, this can be activated in the Conditional Break Criteria tab in Run - Solution Parameters - Edit. You can set the analysis to stop if the convergence criteria at the end of a step (or iteration) exceed some multiples of the allowed convergence errors. Setting the "After step" multiplier to 1 (as you suggest) is usually too strict, especially if you need any results in postpeak. The multiplier for stopping "After iteration" need to be set quite high (e.g., 10 000).
Regards, Dobromil

In postpeak, the results are not much precise anyway (think of many factors that influence localization that are not modelled, e.g., aggregate shapes and positions), and a tight error tolerance would not make much sense.

For pre-peak, several steps with large errors (over 10%) in a row clearly mean the results after are more or less useless (even if convergence is reached in some following steps!), and one has to check the boundary conditions, material parameters, and try to change the step length (typically, shorten, but sometimes a longer step with a larger iteration limit helps to overcome a problematic point, too).

On the other hand, a single step with an error of 2-3% definitely does not make the following results invalid.