Can a user save their work on form, close it without submitting it, and then return to finish and submit it later?

Yes that's possible. You can use either any of this two features.

1. Session Parameter. http://www.jotform.com/features/save-and-continue/. This save to continue feature uses session parameter in which data are saved on the server so it is accessible on any machine using different browser.

2. Autofill. http://www.jotform.com/help/227-How-to-Enable-Auto-Fill-Feature-Save-Form-Entries-to-Continue-Later. This saves the data on the browser local storage so meaning you have to use the same browser in order to retrieve the data to continue filling the form.

Hope this helps!