Madoka never gave up on Sayaka. Not after Homura bluntly told her Sayaka was a lost cause (which she was), not after her "mistake" revealed the truth of what a Puella Magi is, not after Sayaka herself tried to drive her away, not even after Sayaka's final transformation into Octavia.
This is what true friendship is all about. And I don't mind admitting at all, it brings a tear to my eye.
And if you explore the lore, their bonds go even deeper than what was shown in the series. Not just the novelization, either. In a concept sketch for Gretchen, it was revealed that (at least in Timeline 2)...
Madoka (unconsciously?) created a barrier that is the only safe zone from her destruction of the universe...built specifically for Sayaka.
For her to do something like that even in her state, in light of all the other people important to her that would get swallowed up....if that's not true friendship, I don't know what is.
(ending spoilers for The Different Story manga)
if the leaked pictures are to be believed, she also contracts in the story in order to save/resurrect Sayaka.
The last image is Madoka, Sayaka and Homura as Magical Girls, possibly about to fight WN. Even if we know how that battle will play out, it still ends on a hopeful note. Hope is every bit as important a theme in the series as despair.
