How long does a private game session stays after I leave?
Regards
If you want save some Hearts/Blood/Brains you can give it to other hero with help of your friend.
Standart way - your friend create a multiplayer game
Hero1 comes, give hearts to him, or just drops them, then leave server and then you join with hero2 which picks it up
You’d be better off making a friend or using a mod.
If you play a few multiplayer Crucible runs, you’ll more than likely meet at least one person you can tell is a decent human. Become Steam friends with people and add a note to their account name display to remind you (“know it all,” “newer player,” “honest,” “terrible person only good for farming with,” etc. so you don’t lose track of everyone. Profit.
If you’re not super into people, which is understandable in today’s world, mods can help you. I have read that GD Sidekick can be of use, and GD Stash can remove the limitation of character bound items. However, mods can usually accomplish more, so if you don’t have a strong will to resist cutting corners they might end up ruining your experience in the long run.
Easiest way to do this is to use GD Stash.
Although technically it is cheating, and you could conjure Ancient Hearts out of thin air. But if you can restrain yourself… 
It’s ridiculous you can pass them to a friend to then pass them back to you , why these not able to be put in the stash yet is beyond me , total fart about .
Especially self found , it’s a massive restriction .
I don’t use mods etc so GD stash would be far to tempting to abuse so no way I can use that either 