Thank you for the suggestion. Right now, we don't have a way to do this, but we do have plans for the same.
Unfortunately, I won't be able to provide an ETA for this feature, but it is something we're planning to work on.
4 months ago
I was able to get more than 30 unresolved tickets by using the following query, incrementing the page number as needed. The query is all IDs for statuses I consider "open", so everything that isn't Closed or Resolved.
https://YOURDOMAIN.freshdesk.com/api/v2/search/tickets?query="status:2 OR status:3 OR status:10 OR status:11 OR status:12 OR status:14 OR status:15 OR status:16 OR status:17 OR status:18 OR status:19 OR status:20 OR status:21 OR status:22"&page=1
This endpoint doesn't paginate like the other ones (no 'link' header), and you can only go up to page=10, but this is at max 100 unresolved tickets. You could play with the search query to get more tickets to be returned.