I am currently migrating issues from Salesforce to Jira. As attachments could not be imported properly, I imported other fields to Jira and wrote Java code to get attachment files from Salesforce to add them to the corresponding issues in Jira.
Other than closed issues I am able to add attachments with the the API addBase64EncodedAttachmentsToIssue. But for the closed status in Jira I am not able to add them.
You can change jira.issue.editable property of the workflow to true while you are performing migration. This will make the issue editable and you will be able to add attachments. In default Jira workflow all closed issues are uneditable by default.
http://confluence.atlassian.com/display/JIRA/Configuring+Workflow#uneditable_steps