Im familiar with views (and here I include both scientific and mythological views) according to which the universe has a beginning and an ending; and with views according to which it has no beginning and no ending; and with views according to which it has a beginning but no ending.
But I cant recall coming across any view, either scientific or mythological, according to which the universe has an ending but no beginning.
Now it doesnt surprise me that thatd be the least popular of the views. Despite the admonitions of Epicurus and Spinoza, we tend to find the prospect of future nonexistence more depressing than the prospect of past nonexistence; so objections to finitude, for those who have them, are more likely to focus on the future than on the past. Furthermore, counting down from infinity likewise seems more objectionably paradoxical than counting up to infinity; so objections to infinitude, for those who have them, are more likely to focus on the past than on the future.
All the same, its a big old world with a lot of people in it, and the space of possible views does tend to get populated, so Id likewise be surprised if nobody had ever held the end-but-no-beginning view. My bet is that someone has. I just dont know of any example.