You can solve it like this, if you want to display a certain block only if it has content. Hope, this is what you’re looking for.
Example index.html.twig
{% set _block = block('dynamic') %}
{% if _block is not empty %}
{{ _block|raw }}
{% endif %}
Example part.html.twig
{% extends "index.html.twig" %}
{% block dynamic %}
Block content goes here.
{% endblock %}