How do I save a fillable pdf and make it unfillable after saving it?

There are several ways to make a form unfillable. The easiest is to use a script to set all the fields to Read Only. This can be done with a script on the PDF. The problem is determining when to do it. Do you want this to happen every time the form is saved? or only when the form is complete? 

One technique is to lock the fields on a digital signature. The signature field has a special action just for this. 

Anohter technique is to flatten the form. But this can only be done from a folder level script, i.e. a script installed into Acrobat. So this one only works for you, not anyone else filling out the form.  

Hi,

You  can accomplish this by adding a button with a javascript action to the form, creating a new action with the action wizard tool and running a javascript manually, or as a batch sequence.

Also I've seen this question answered before, where the solution implements a signature field in the form.

When this field is signed,  it saves the  whole document as read only.

In addition, you may also consider to protect the document from editing with password.