Is it possible to track who has not filled out the form that we've sent it to?

There might be a workaround for your concern. Do you have an email address field on the form you're working on? (May we know the form you're working on, please?)

If you have, will the submitters enter the same email address where you have sent them the forms? If it is, then this workaround might work for you.

The first thing that you need to do is integrate your form with Google Spreadsheet. 

You can access the Google Spreadsheet with the link provided after the integration:

On the spreadsheet, create a separate sheet.

Then, on the first column of the new sheet, copy the list of email address where you sent your form.

Next, on the second column of the new sheet, you will use the spreadsheet formula below.

The formula: =IF(COUNTIF(Submissions!C$2:C$101,A1),"Yes","No")

The formula above is just for the first row, you will just copy it onto the next rows of the second column, here's how:

Above, you will see that a row in column 2 of the new sheet will show "Yes" if the email address exists on the Submissions sheet's email address column.

I hope this helps. Let us know if you have questions with any of the instructions given above or if you have any other questions. Thank you.

Thank you for this.  So, this would only work if we sent the form to someone via email?  To confirm, this wouldn't work if they completed the form through a link on a website?

That is correct. This workaround will only work if you have the list of emails where you've sent the form. It will not work if they completed the form through a link on a website.