Core breadcrumbs in Drupal 7 are implemented in a way that they only work for the current page. So to achieve this with core, you would have to "simulate" a page request and somehow harvest the breadcrumb. This is probably painful and not worth the effort.
In Drupal 8, you have breadcrumb builders that take a route match as an argument. This route match can be any page. So yeah, what you want would be possible in D8. But you are in Drupal 7.
In Drupal 7 with Crumbs module, breadcrumbs are calculated independently of the current page. You can see this in action on
crumbs_get_trail() accepts a
$path argument, which can be any path you want. But this gives you a "trail", not a breadcrumb itself.
Unfortunately there is no one-liner to give you the breadcrumb for any page.
But here is what you can do:
// Create a local version of the Crumbs service container.
$services = new crumbs_DIC_ServiceContainer();
$page_info = $services->page;
$page_info->path = 'node/123';
// Optional: Set display settings.
$page_info->minTrailItems = 1;
$page_info->showFrontPage = TRUE;
$page_info->showCurrentPage = TRUE;
// Now choose which piece of information you want.
$trail = $page_info->trail;
$breadcrumb_html = $page_info->breadcrumbHtml;
$breadcrumb_data = $page_info->breadcrumbData;
$breadcrumb_items = $page_info->breadcrumbItems;
$raw_breadcrumb_items = $page_info->rawBreadcrumbItems;
This can be starting point for you to play around with.
If you use Crumbs for this purpose, you get the full package: All your breadcrumbs will now be controlled by Crumbs. Maybe this is what you want, or maybe not.
I am not aware of other breadcrumb-customizing modules which provide this functionality.