EmailLabs has 12 tips on what you can do to re-engage the inactive subscribers for your newsletters, panel or promotional marketing :
1. Use special offers
2. Survey subscribers
3. Allow profile updates
4. Understand their demographics/profile
5. Try different send dates/times
6. Modify the frequency
7. Create different content
8. Try different formats
9. Test different styles of subject lines
10. Monitor seed/proof lists
11. Send a postcard through regular mail
12. Move re-engaged to active status
Source & description for each tip : [EmailLabs]
Also read : 15 Tips For Improved Subject Lines.