For example, look at The Legend of Zelda: Ocarina of Time. In that game, the main way of increasing the survivability of Link is to find Heart Containers and Heart Pieces, which increase the number of hearts Link has. However, that is not the only way. It is also possible to effectively increase Link's total amount of life by carrying Red or Blue Potions, which fully restore the life gauge. On top of that, there is a special blessing Link can receive near the end of the game that reduces all damage taken in half. Link starts with 3 hearts, but that can grow to twenty. With four potions, it becomes 100 hearts. With the special defense on top of that, Link effectively can take 200 hearts worth of damage before dying. In order to even challenge a fully stocked up Link, an enemy would need to dish out 8-10 hearts worth of damage with each hit.
The end result of this is a difficulty curve in the game that is skewed towards the beginning. The early stages in many Zelda games tend to be the most lethal. The final parts of the game tend to be the easiest, since it is hard for Link to actually die. This is backwards. The game should be easiest in the beginning, so that a new player can become accustomed to the gameplay and drawn into the story. The later parts should tend to be more difficult, so that the player feels challenged and engaged. As it is, many Zelda games can be frustratingly hard early on and anti-climactically easy once you get to the final battle.
This is sometimes justified by saying that it lets the player choose their own difficulty setting, but I don't think that actually works in practice. This setup forces the players who want an easier time through the game to undertake what could be the most difficult and time-consuming task in the game. It makes the dedicated completionists get stuck with an easy trip through the game. And it makes the early part of the game, before these radical power increases can be acquired, equally hard for everyone.
The problem would not be that bad if the increase in defensive power is more linear. It is easy for a game developer to take into account a gradual, steady increase in character life by gradually stepping up the strength and numbers of enemies. The really problematic element is the doubling of defense. A doubling of defense is the same as doubling the size of the player's life meter. It is something that has a drastic effect on the character's longevity. When game designers balance the difficulty of the game to assume that the player has not collected every item or power, a defense doubling item can throw that balance completely out of whack.
There are plenty of other game series with similar defense mechanics to the Zelda series. The Mega Man series has plenty of games where the player collects Life Upgrades, armor that cuts damage in half, and Life Tanks that fully restore health. The Metal Gear Solid series also has life increases, healing items, and optional equip-able body armor. So, this kind of problem can potentially happen in many other series than the Zelda series.
One way to keep this problem in check is to avoid straight multipliers. If the healing power of potions was a simple set small number of hearts (like how a ration in MGS heals only a set amount of health), then having a potion or not wouldn't have as much effect on game balance. Eliminating the huge effect of the defense doubling would also help limit the wild difficulty swings.