Well good, now I'm less concerned about my hypothetical scenario. But to be clear, I'm not concerned about people sending in fraudulent or forged ballots. I'm talking about a third party generating fraudulent applications based on whatever personal information they can find, which then results in legitimate voter(s) being put on the list of people who were sent mail-in-ballots. The legitimate voter should know that something is up when they get an unsolicited ballot in the mail, but they may not know that they have to bring it with them when they vote, and/or deal with the process of voiding it. That may be enough of an inconvenience or delay to make some voters just say to heck with it.
As to the who and the why, I'm not going too far out on a limb to suggest that some people would like to disrupt this election as much as possible. Even more so if they could find enough information to create a targeted disruption or inconvenience for certain demographics who tend to support a particular political group or policy. I'm not claiming any of this has happened or will happen, but I'm just wondering if it's a possible vector for mischief.
Edit: as far as the signature on the form, does the election office actually verify the signatures against whatever they have on file?