If you are a Ph.D. student writing a cover letter for a job application, there is no need to state that your financial support has ended. Presumably, you are applying for a position for which you will be paid. In that case there is no reason to let anyone know that your financial support has ended.
Your cover letter provides an opportunity for you to not only present your most winning and relevant qualifications but to also demonstrate that you know something about the company and position. Use the space to share your interest in the role and why you would make a good addition to the team. Share some notable information about your work – either as Ph.D, or in any past or current roles that tie to the job you are applying for – that would spark the interest of the reader. Information about financial support has nothing to do with the role or your ability to perform. Focus your energies on the positive things you can offer and how you will make a difference. There is almost never any need to mention anything about your financial state in any cover letter.