No the sky isn't falling, that's foolishness. But it is interesting to consider how people used to think about the heavens.
In biblical days the sky was referred to as the "firmament," and firm they thought it was--a smooth curved object made of a thin solid material.
The word firmamentum is Latin and a translation from the Greek stereoma, meaning solid dome. That in turn is a translation from the Hebrew rakia, meaning a thin metallic sheet. The sky, they thought, was a close-by, semi-spherical solid dome made from a thin sheet of metal that covered the flat earth, coming down to meet it all around at the horizon.
So when the Book of Revelations in the Bible speaks of the destruction of the Earth and sky, it says--reflecting the then current cosmological ideas and language--"And the stars of heaven fell unto the earth...And the heaven departed as a scroll when it is rolled together" (Revelation 6:13-14).
In other words, about 2000 years ago people thought the world would end when the thin metal sheet that the sky was made from rolled up (spro-o-o-ing), and all the glittery little lights that stuck to it fell off. Now we know that the Sun, one of those little lights that just happens to be realtively close, will eventually burn most of its hydrogen into helium, become a red giant, and simply envelop the Earth.