It is possible to have a large form that, as the client fills it out, becomes a draft, which he can later retrieve and continue filling out.
Hi Gustavo - Welcome to the Atlassian Community!
Not during the Create issue process (that is when you are creating/submitting the ticket).
With the out of box Form feature in JSM, here is the link to a way to edit customer's submitted form.
Synopsis for your reference below
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Once a form is submitted, you may need to open customer edits so you can collect more information from a customer
Open customer edits on a form
You may want to open a submitted form for a customer to edit in the portal. If the form is locked, only project admins will be able to do this. Learn more about form settings
To open customer edits on a form:
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