I don't know about German law, but in Finnish law you can only appeal to the trial period if you have an acceptable reason related to the trial period. For example, if the employee isn't performing well, that is a legal reason to annul the work agreement during the trial period. But selling the business to investors or having financial difficulties because of the economy are not acceptable reasons, since they are not related to the specific recently-hired employee.

It cuts both ways: the employee can walk out during the trial period for reasons such as feeling like they didn't fit in, or the work being different from what they imagined. But if they merely find a better-paying job elsewhere, they cannot invoke the trial period but have to give notice in the usual way.