I wouldn't call it "stealing" but yes, he wrote a lot of what we today would call historical fiction. He wrote about Julius Caesar, the Greek siege of Troy, and did an entire series on the English monarchy.
He didn't steal stories, but he was inspired by political and social events. For example, the story of King Lear and his three daughters appeared after newspaper report of an old man who had three daughters. The eldest two tried to have their father declared incompetent to control his assets. His youngest daughter took the matter to court and successfully defended her father's right to conduct his own affairs. Every writer is influenced by what they see, read, hear, and experience in the world. Shakespeare was no different.