What does “The man that once did sell the lion’s skin While the beast liv’d was killed with hunting him” mean?

I came across the following sentence in the context of four professional men discussing a plot to retrieve their lost $1 million, swindled from them by a nouveau riche American banker in Jeffery Archer’s novel, “Not a Penny More, Not a Penny Less”:

The man that once did sell the lion’s skin
While the beast liv’d was killed with hunting him.

The line reminded me of a Japanese proverb, “ミイラ取りがミイラになる - A mummy searcher always ends up as a mummy,” which I think is close to an English saying, “Go for wool and come home shorn.”

What is the exact meaning of the above two lines? Is this a popular English metaphor?

Why is there no period at the end of the first line while the second line starts with the capital?

Is it wrong to rearrange the sentence as follows?

The man that once did sell the lion’s skin was killed with hunting a lion while the beast liv’d.

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As FumbleFingers pointed out in his comment, it's from Shakespeare's King Henry V (Google sample). Seeing it in the context of the script (with its original punctuation) makes it easier to understand. The man sold the lion's skin while the lion was alive, but was killed by hunting the lion. The meaning behind it seems to be that the man sold something he did not have (the lion's skin) and failed to get it (died). Not only did he fail to deliver, he was ruined by his folly.

This could be used in two different ways in the novel (I'm not familiar with it, so I can't say which it is):

  • The banker swindled the men (akin to selling a lion skin he does not have) and will be punished for it (killed in the hunt)
  • The four men are depending on their money that they have not yet gotten back from the banker, and pursuing it will be their downfall.