It's going to be a wonky class that goes down really fast
You want to make a Barbarian, but instead of having armor class, they'd basically have a once per long rest 50% of their HP shield.
Now ask yourself, would you rather:
Get hit only 10%-20% of the time because you have a really good armor class. This means you're getting hit 80-90% less than others.
Be able to take 50% more hits than other people, but that 50% extra can't be healed in any way.
It won't be long before your easy-to-hit tank is down to their normal hit points and at that point they're just a Barbarian with a terrible armor class. The only thing your HP sponge would be better at is tanking enemies that have incredibly high hit chances, to the point where a normal Barbarian would reliably get hit as well, or enemies with terribly low hit chances, to the point where honestly anybody could be tanking them.
You would have to add insane amounts of hit points to make this trade-off worth it. If you can somehow do that, you've now unbalanced the AC vs Saving Throws balance, because your extra HP means you're essentially "good" at any saving throw that ends up dealing damage, you have plenty of HP anyway.
And that would come on top of having to prevent the player from simply increasing his AC by multiclassing into something, or taking a feat, to get a better armor class, or having somebody cast Mage Armor on them.
Long story short, this is an idea that is never going to be balanced.