If you put /attribute @p minecraft:generic.max_health base set 1 into a repeating command block that is always active. Then, type /kill in chat to kill yourself. Next, you want to respawn. This will make the player's health bar show half a heart. Then, fall off of a cliff that is at least 10 blocks high. If done correctly, the play will take fall damage but won't die even at half a heart.
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This is technically a duplicate report, and it happens in unmodified vanilla Minecraft
Looking at the video you seem to be playing with OptiFine, which is a modified minecraft client. If the issue is still present in vanilla, please update the post to showcase it.