Can my dad apply for life insurance this late?

My dad received a letter and application for life insurance for $25,000 coverage. He got that about a month ago but didn't apply for it. He has no life insurance at all The letter said there is no medical examination required. The application deadline is 2 weeks from now. My dad though, is in the hospital right now and likely to die from liver failure. Is it possible to still fill out that application and have him sign it and get the $25,000 if he dies?