There has been instances when you plan to upgrade SharePoint 2007 to SharePoint 2013 and using custom workflows which are designed by SharePoint Designer.
If we follow the straight upgrade process like upgrade the database from 2007 to 2010 and then upgrade to 2013 you will not be able to edit the workflow not update them.
Here is the process which need to be followed to make sure we can continue using those workflow in 2013 and can update and edit them without issues.
1. Take the back of the content DB from the SQL server.
2. Restore the backup on SQL server for the SharePoint 2010 farm.
3. Create a new claims based web application.
4. Attach the content database to this web application – mount-spcontentdatabase
and make sure we follow the process to migrate the users from classic to claims, reference -http://technet.microsoft.com/en-us/library/gg251985.aspx
5. open the site in SharePoint Designer and edit the workflow and republish it.
we have to do this because sharepoint designer 2007 workflow are aspx based and 2010 will be form based and hence the upgrade needed.
6. Now take a backup of the database and restore it on 2013 SQL server farm.
7. Attach the database to SP2013 web application using the command mount-spcontentdatabase.
8. Open the site in designer and we should be able to edit and update the workflow.