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I'm not sure if I understood you correctly. When you say "incomplete forms" are you referring to incomplete payments done to your purchase form? If this is the case, you can check the following links to know more about it, and yes you will see the email used.
The user needs to click the "Submit" button for the form to have a complete submission. If they did not click it, no submission will be received.
Let us know if you need more assistance on this.
Thanks for the reply.
What I want to do is to be able to send a message (through the mailchimp plugin) to any people who have started the form but not completed it.
So how do I retrieve unfinished form emails?
Unfortunately it would not be possible to know if someone had entered an email to your jotform and then closed the tab without completing it.
The reasons are many, such as the option of privacy, since they did not yet selected to share that info with you.
The only way that I can think off the top of my head would be to use one jotform to ask for the email and then send them to another jotform to complete it.
If you apply this next technique, it would also allow you to see the data that they have entered, but not submitted to you: How to Save Forms to Continue Later
To summarize: You will not be able to find the email addresses of people that did not submit your jotform so far, but you can, by applying the steps above see the emails that were to submit, but did not actually submit it.
Do let us know if you have any further questions.