It's rare, but an account can be suspended for a protracted amount of time when all other attempts at reasoning have failed when it comes to a certain type of behavior. It's not always behavior, though; There's a few things I need to explain to really lead up to a proper answer to your question.
My apologies for not being able to make a
tl;dr; version, how we've used suspensions in the past has changed over time - leaving some curious artifacts such as the one you found.
The length of suspensions
As you know, users that are under the age of 13 can't participate on our sites, as per our terms of service. The way that we used to handle a disclosure from someone that they were only ten years old was to suspend them until they were old enough to participate. That required us to be able to suspend someone for longer than a year, so the maximum time the system would accept when a suspension was issued used to be quite high.
We changed that, moderators are no longer able to suspend accounts for more than 365 days. The community team now deals with reports of users under the age of 13, and we handle it quite differently.
In order to issue a suspension longer than a year, you now must have developer access, and that suspension must be network-wide, there's no other way to do it. Yet, some long term suspensions issued two years ago are still in effect - so you might see some inconsistencies.
If you see that an account is suspended network wide for more than a year, it's a strategic move on the part of an employee with developer access to bring something disruptive under control.
Why would you suspend an account longer than a year?
If this has happened, it's generally because a user was being very disruptive, was suspended, and created new accounts in order to continue throwing the chess pieces around the park rather than sit down and play chess like everyone else. With new systems to keep those people out rather quickly in place, we don't generally do this any longer, we'd much rather have moderators simply remove accounts that exist purely for negative reasons, or should never have existed in the first place.
There are times, however, when people on the community team use the network-wide penalty box as a tool to help contain something raining down disruption on several sites, think of it as a metaphorical lasso. Still, new systems in place are making this less and less common.
But, there are some left over that were handled a long time ago, and having this discussion tells me that I need to make time to write a query to fish these out and review them. They might not all require action, but they should be reviewed in light of changes that we've made.
What happens to users after they've been suspended for a year but the problem persists?
This depends on the user. In cases where the user has no contributions, we'd inform them that we feel it's in our mutual interest for them to just not return to the site, and remove their account. In other cases we might try issuing another suspension. As long as we can see hope for the user participating positively, we will do our best to work with them, and try really hard to not lose good contributors.
Remember, we once didn't have suspensions, the thinking was that if a user was that much of a problem, they should probably just leave the site. That thinking changed quickly as we learned that very awesome people sometimes just have difficulty controlling their emotions, or folks learn that using sock puppets was a pretty bad idea and just participate honestly.
When used correctly, suspensions should just freeze the action, let us inform the user of what's wrong, how they might fix it and lift automatically after a short time. Using them for anything else is generally a bad idea, and we've moved away from that over the years.
Still, you're bound to find a few still laying around, even after I go dig them up and review them.
Just remember - we can't discuss things surrounding a specific user's suspension, as it's between us and that user. There might be exceptions, but those are called exceptional for a reason.