First of all - absolutely love the Don't Starve games. I normally wouldn't bother writing on a forum like this, but these crashes are really bothering me, especially since the game is so awesome.
I've gotten this one several times on my XB1. While playing, if you press the Xbox home button while moving around, the game freezes. (Or actually seems to kinda pause, but you have access to move around in your crafting menu.) You can usually get out of it by opening the map, but other times (and this might be another crash?) it causes the game to close and boots you back to home screen. In both cases, when you try to reload the game afterwards, the save file seems to be corrupted. You just get a black loading screen then it boots you to the home screen.
1) Select Don't Starve: Shipwrecked 2) Select Walani as a character. 3) Proceed to at least day 10 then move around and press the Xbox home button. (My latest one happened on Day 17.) 4) When you get back to the game it looks paused but you can move around in your crafting menu. You can (usually) get out of this by opening up your map but there have been times it has crashed at this point. Though to reproduce this issue, when the game is 'paused'/frozen in that state, quit the game from your Xbox menu. 5) Relaunch the game and try to load that save file. Results: When you try to load that save file you get a black loading screen and then it boots to the Xbox home screen.