WMG / Wooden Overcoats

Eric Chapman is a distant relative of the Funns.

It’s stated in the first episode that the founder of Funn Funerals was a serial bigamist. Perhaps a child of his second wife left the island, and became an ancestor of Eric?Plus, one of the central themes of Antigone’s namesake is that she refuses to take sides in the conflict between her two brothers, both of whom she loves.

Eric Chapman is immortal.

Specifically of the "Cannot be killed" variety. This is how he's been able to do everything and be everywhere "a long time ago" despite not seeming to be very old physically, how he survived Jerry's bomb despite the fact that Jerry was aiming to kill him specifically (outside of pure luck) and how he's so incredibly wealthy, having saved up money for potentially centuries. Furthermore, he is the only one who adores Antigone's Memento Mori chocolates; he claims this is because he has bad taste, but it would make sense if he loves them because they simulate a death that he will never be able to experience. Additionally, he would then be exactly the kind of clientele who would benefit from the Smart Coffin, a device which comforts and rescues people who have been buried alive. This is also how he keeps so happy even surrounded by death and grief—he's lived for so long that he's numb to it. Perhaps the story he told Georgie that happened in 1928 was something he actually witnessed himself. As a final note, the reason why it "could get awkward" if the British government got involved in rescuing him and Antigone in "Undertakers Underground" is because the government is interested in obtaining him for his immortality.

Piffling Vale will end up with no funeral home at all.

By the S3 finale, Rudyard and Antigone are beginning to tentatively discuss the possibility of going into a different line of work, and by the end of the episode Rudyard’s been offered a job working with the mayor’s archives, which he seems enthusiastic about.

Even without Chapman’s rivalry, it’s established that the Funns were already struggling financially and it’s reasonable to assume they wouldn’t necessarily have chosen the funeral business, had it not been in the family. Taking all this into account, along with the fact that the writers have said the 4th series will be the last, there’s a decent possibility that they’ll decide to pack it all in by the end of the series.

As for Eric, fans have pointed out that funerals seem an odd choice for him, given that his talents would likely be suited to planning celebrations for less sombre occasions, such as birthdays or wedding anniversaries (although we can likely assume that his choice relates to something that happened... a long time ago.)

Eric’s brand of funerals tend to have a celebratory air about them, which is fine for people who prefer to frame it as a celebration of the deceased’s life, but not so much for anyone who expects a more sombre affair. It’s also been established that Eric has a hard time understanding or dealing with others’ grief.

After the events of ‘The Sunshine Treatment’, Eric might come to the conclusion that he’s not as equipped to deal with bereavement as he’d assumed, and that his talents would be put to better use as a standard party planner (or running one of the various establishments he’s already set up in the village). This revelation would coincide with the Funns deciding to close up shop, leaving Piffling Vale with no funeral home to speak of, and rendering the Funn/Chapman rivalry ultimately All for Nothing.