;) Yes, indeed, 'Eucatastrophe' is in fact a literary device that leads to a happy ending, when it seems almost certain that an unhappy/negative ending is nigh. As so often claimed by scholars, this device was probably 'developed; by Prof JRR Tolkien (please see links below) and indeed, in a number of Tolkien's works, most notably the Lord of the Rings, eucatastrophe is employed effectively to brign about victory for the forces of 'Good' versus Sauron (i.e. 'Evil').
Since eucatastrophe is a literary device, or technique, I am not entirely sure how you mean if it 'relates' to us-- do you mean if we have examples of 'eucatastrophe' in our lives today, in reality rather than fiction? Or do you wish that examples of eucatastrophe in contemporary fiction or cinema be given here?
In my view, as far as 'real' life/existence is concerned, one rarely experiences such a lucky chance or coincidence; but in both contemporary fiction and film/cinema, some pretty good examples of sudden and dramatic twists of a 'favourable' nature are strongly in evidence in the ending to the Harry Potter series (originally written by JK Rowling as well as the Hollywood versions) -- indeed, although Tolkien also wrote in the fantasy genre, some of the examples of eucatastrophic events (not to be confused with 'deux et machina') utilised by Rowling tend to go ather to far in my opinion.