If a company I interviewed for called my former boss, can my former boss say why I was fired?

I was fired under false pretenses, which I might go to the Texas Workforce Commission about. In Texas, you don''t need a reason to fire someone. After being fired, my company said I stole property from the company and gave the exact time of my breach of security to get intellectual property that is the company''s property. I did not do so. For this, I was denied the full two weeks of pay I was told I would receive. Can my company/boss, who I do not have as a reference on my resume, give the full reason of my firing, including the false accusation that I stole intellectual property?