What happens when the owner of a club has abandoned and deactivated their account on Fanpop?

The creator of a spot/club is not really considered the "owner".
On the FAQ page the F4 state that
"Fanpop is all about community and sharing. We would hate to get into turf wars and territorialism on our site, so we've decided it would be best if each club was a democratic state."
Each spot that has been created in fact belongs to every member, not just the original creator.
"Everyone gets to contribute videos, links and images and anyone can propose artwork for a club (banners and icons). The person who creates the club just gets to kick it off for all their fellow fans to enjoy."

So just because the fan who created the spot is no longer an active Fanpop user or has been deleted there is no reason for the spot to not exist. There are still other users who are contributing to and appreciating the content on the spot.

Well it's not necessarily dead. There are plenty of active spots where the original creator has abandoned it. You just have to contact one of the F4 if you want something changed =]

As others have stated, the club isn't necessarily dead because the club creator has left. Any other member can still contribute by adding images, videos, polls, articles etc.

In terms of changing the icon and banner, it depends on how many members the club has. Clubs with 10 or more members have a mechanism to let those members vote for icon and banner changes. With a smaller club, you'd need to message one of the F4 asking them to change the images, though it's still best to ask the club members their opinions first.

I don't know if there's a mechanism for changing a club motto. I think you'd have to message the F4 in that case.