Can users save forms and come back later to complete and submit it?

Yes, this is possible to do, please check the following guides that will help you doing so, the first one for classic forms and the second once for card forms: 

https://www.jotform.com/help/97-How-to-Save-Forms-and-Continue-Later

https://www.jotform.com/help/495-Setting-up-the-Continue-Forms-Later-Feature-in-Card-Forms

I hope this helps.