Can users save their forms and then finish it later?

Is there a way I can allow a user to save their form in the middle of filling it out and then finish it later

Yes it is possible to have users saving their forms and continuing to fill them later. For that you need to create 2 forms, one that will be used to create a session and the main form.  

You can see here more details on how to implement this solution:

http://www.jotform.com/features/save-and-continue/?

You can also test it here:

http://form.jotform.co/form/32927314628862 

If you need further assistance please let us know as we're here to help.