The two are polar opposites. Bill, hardcore, unemotional, and trusts no one. Frank cries a lot, is sentimental, and openly homosexual. Both have somehow managed to survive in a post-apocalyptic world, despite fungi zombies, marauders, food shortages, the government, etc.
To keep the summary short and simple, Bill finds Frank stuck in one of his trap holes, and decides not to kill him. In fact, Frank talks Bill into letting him come into his compound, have some food, and a warm shower. The two end up complimenting each other well, and in fact, fall in love. What we have in this episode is a very bleak world, humanity falling apart, and two individuals accomplishing the impossible—falling in love. But not only do the two fall in love, they stay in love until the end of their lives.
Most romances, if successful long-term, end in tragedy, as one partner almost always dies before the other. With Frank's health failing, he decides it is time to end his life. Bill tells Frank at the end of their last meal together:
This isn't the tragic suicide at the end of the play. I'm old. I'm satisfied. And you were my purpose.
Bill decided to also end his life, so that neither would have to be without the other. It is poetic in the sense that despite the bleak post-apocalyptic world in which they lived, they were able to be happy together. They lived apart from other survivors, so they mostly only had each other for companionship. Bill had no reason, no purpose to continue his life without Frank.
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