One theory of how Longacre Doubling was created is the punches with the design elements (stars, letters, numerals, etc.) were the same shape and slightly larger than the design element which created a "ghost" around the design element when it was punched into the Master Die. So every Working Die created from these Master Dies would have the same Longacre Doubling.
Frank Zapushek explains Longacre Doubling rather well here. Quote:
From about 1836 till 1886, the main design elements where (sic - so many people confuse 'were' and 'where') put on the galvano and a reducing lath transferred the design onto the master hub. The master hub was raised or incused (sic - 'incused' means 'pressed into'), because the metal was removed to leave the design of the galvano. The master hub was then used to make a master die. The master hub was pressed into the die steel to form the master die, so the master die had a recessed design.
The engraver would then use a punch to place the outer design on the master die. If the engraver wanted to give the punch more detail, he could shave the sides of the punch, leaving a lip on the punch.
If the engraver hit the punch extra hard, the lip would be incused into the master die. Thus causing the Longacre doubling on the working hub, the working die and the coin.
The second theory is after the design elements were placed on the master die, the engraver would go back over the design moving the punch just a little. This would place a small lip on the die to help the metal flow into the die.
It is also believed that Mr. Longacre felt this would give the dies a longer life and provide more coins from each die. Helping to reduces the expense of die production.
Both theories would produce a rounded doubling, but it is not considered a doubled die because the master die is only hubbed once and there is no separation of the serifs.
Not all dies produced the “Longacre Doubling”. On those that did produces (sic) the doubling, it will slowly disappeared (sic) as the die strikes more coins. Or if the die is polished for any reason. So, if a coin as (sic) the full doubling like this coin, it must be a very early die stage.
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