Video games where you adventure into a harsh setting, try your hardest to survive and slowly develop your abilities but then inevitably die are often called Rogue-likes. This is because one of the first games that offered this style of play was called Rogue.
These are interesting games for families, not only because their difficult nature leads to shorter sessions, but also because they foster perseverance and coping with losing. After dying you are sent back to some sort of central village where you can choose upgrades for your next attempt. The incentive to play again once you have been killed is usually that you start with some more equipment or skills.
In this way, by belligerence and a slowly learned understanding of how the game world works and how best to survive, you incrementally get a bit further each time you play. Here are some really good roguelike games for families:
This list includes 249 games from the last 44 years, with 1,998 likes. They come from a range of different genres and play-styles and are all good games if you want to cope with losing.