Post-manufacture. The stamps (in coil rolls) were more than likely affixed to mail with a mechanical device of some sort. They typically have a cutter blade that is supposed to "tear off" the stamp at the perforations and a moistening sponge that allows the gummed stamp to stick to the envelope, but sometimes (due to misalignment, etc.), it results in the example shown above. The US Postal Service used to have vending machines (no more) that did exactly the same thing on much more recent issues, too. They are generally less desirable to collectors.
Here's a period ad for one of several such devices that were in use back in the 1930's and 1940's:

By the way the example of the 1-1/2c stamp shown above has a partial cancellation from the New York, NY "Grand Central Station" branch.