Board games, traditionally, sit on a shelf, with no knowledge of when they were last played, or what happened in the last session. They do not care if you play them once a day or once a year. They have a very well defined goal that leads players towards it in even the most open-ended examples. Most board games, including solo and cooperative games, have a defined win and loss state, however nonsensical to the theme it is.
Legacy games are board games with memory. You gradually unlock their contents over a series of games, and the decisions you make with that content permanently change the nature of the game being played. For example, you might tear up a card, or place a sticker on the board. At the end of the campaign, you either have a unique version of that game, that you can jump back into whenever you like... Or something completely useless for all time, depending on the nature of the game and how the board looks at the end of them. They still have a win and loss state, though the addition of unlockables can lead players to not prioritize things other than the win or loss state. But, ultimately, each session of a competitive legacy game has a winner, and a cooperative legacy game the group either wins or loses each session.
But why should a game that remembers the history have a defined win and loss state? If the game ends, and progress is tracked, with the intent that you'll pick up the game in the next session, do these sessions necessarily need to define winners and losers, either individually or as a group? And if there are no winners or losers in a single session, does the campaign need to end with a single winner or determining if the group won or lost the campaign if cooperative? For that matter, does the campaign ever need to end?
Sandboxes are an oft-talked about part of the video game space as shorthand for 'you can do anything you want to do.' This usually means 'you can do whatever you want, in whatever order you want, and the actual goal of the game is just a suggestion.' How true this is could be debated - it's hard to get married and settle down in a video game where the only meaningful interaction you can have with NPCs is to shoot them or run them over, but within the framework of the mechanics provided doing whatever you want is usually pretty open.
Animal Crossing, as a franchise, is one of the most open-ended videogames I can think of, removing even the open-world 'There's an endpoint here, but it's really only a suggestion of something you might want to do at some point.' Yes, you have a bucketful of debt to pay off, but that's never presented as the end goal of the game, more something to do as you play to increase your house size, and with that the amount of space you can use to decorate with furniture. It's a little signpost to give a new player direction until they figure out what they want to do. Other games go beyond that in presentation, but even Minecraft acquired a definitive 'ending' - a definite goal to achieve - complete with end credits when you do.
If you plant a tree in an Animal Crossing game, it grows over several days, and then enters a cycle of bearing fruit every few days, which can then be sold. Those days aren't virtual, tied to a usual video game day/night cycle, but are real-time, tied to the real-world clock. You plant a tree while playing on Monday, then when you play next week that tree will have fully grown and now be able to drop fruit some of the time. Weeds grow each day, if you pick them then the town remains weed-free but if you don't then the town keeps accumulating weeds. Again, not virtual days, but real-time days. Shops have opening hours and if you happen to not be playing during those real-world hours? You aren't getting any shopping done that day. If you use a shop frequently enough, it might expand into a bigger or better form, and some new shops might appear if your actions make your town seem like a good prospect, for example, if you do a lot of weeding then a garden centre might open.
Seasons change, and with that bugs and fish that can be caught, and holidays happen, all according to the real-world calendar. If you spend a week without playing, you'll have 7 days worth of weeds to pick or leave, and your fellow villagers might ask where you've been. It's a lifestyle game, not in the sense that you have to dedicate 20 hours a week to the game to keep your skills sharp and stay at the top of the leaderboards, but in the sense that the game asks you to spend 20-30 minutes with it each day, incorporating it into your daily routine. The lack of consequences is palatable - It ultimately doesn't matter if you win, lose, or ignore a fishing tournament. You'll be rewarded if you win, and it's a once a month or so opportunity, but if you'd rather just go about your usual routine of picking weeds, collecting fossils, and checking the shops? The game doesn't mind. You do you.
Could that sort of concept work in a Legacy board game? Obviously without designing, developing, and playtesting - by no means a trivial task - it's impossible to say for sure, but I do sometimes think about the months or even years that some people put into Animal Crossing titles, the sorts of themes that board games sometimes visit without any logical reason why there should be a single winner, and the fact that one of the reasons I play board games is to spend social time with friends and family. And that coalesces in my mind, making me wonder if board games have just barely scratched the surface of what the Legacy concept could offer the medium.