When speaking about death, 'almost' and 'close to' are pretty much the same thing.

In this term, near means close to. Considering your question has two options to choose from.

In the phrase "near-death experience," the word "near" means "close to." It indicates that the person was close to death but did not actually die. So, in this case, "near" suggests proximity to a life-threatening event, but not quite reaching it. Example: A near-death experience refers to a situation where someone almost died but survived. Tip: In English, "near" often implies something that is very close to a particular point, but not necessarily reached. It can refer to both physical and figurative proximity. In this context, it's used figuratively to describe being close to death.