Can MySql cause a Windows server to shutdown unexpectedly?

I hope this is the right place to ask this question.

For the 3:rd time, my server where my Mysql instance is running simply shutdown unexpectedly, this time, causing my tables to be corrupt as I had ALTER statements running.

While in contact with my hosting company, they deny that it is a hardware failure (they have done test that showed no hardware failure) and says that MySQL uses up all resources which causes the server to just shutdown. In my mind, the MySQL instance would shutdown unexpectedly, not the server itself but maybe im wrong.

My question is simple. Could MySQL cause the server to shutdown unexpectedly?

There are nothing in the error logs of either the server, or Mysql. Just that the server had shutdown unexpectedly.

Has anyone had this problem where MySQL causes a unexpected server shutdown?