nonhomeless

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*ḱey-
15. Proto-Indo-European*ḱóymos
16. Proto-Indo-European*teḱ-
17. Proto-Indo-European*tḱéytibf.
18. Proto-Indo-European*tḱey-
19. Proto-Indo-European*tḱóymos
20. Proto-Germanic*haimaz
21. Proto-West Germanic*haim
22. Old Englishhām
23. Proto-Indo-European*lewh₁-
24. Proto-Indo-European*lewHs-
25. Proto-Germanic*leusaną
26. Proto-Germanic*lausaz
27. Old Englishhāmlēas
28. Middle English*homles
29. Englishhomeless
30. English todaynonhomeless

From non- + homeless.