If the initial position of [Conway's game of life][1] is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.  
[![enter image description here][2]][2]

*Question*: Can we prove that such a vanishing is not possible for any $n>100$?

**Edit**: The sequence [A061342][3] gives the period $p_n$ of the stationary component of the final pattern for an initial line of length $n$. But for $n \in [84,1000]$ we have $p_n \ge 2$, so the pattern must be non-vanishing in this case. But we observe (after [Nathaniel Johnston][4]) that for $n=500$, gliders are produced on the boundaries after $471$ steps, but $471<500$, so this must happens $\forall n \ge 500$.  
It follows that the answer is **yes**.  

*Improved question*: Is the *stationary component* non-vanishing for any $n > 1000$ ? 

*Stronger question*: Is $p_n \ge 2$ for any $n > 1000$ ?


  [1]: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
  [2]: https://i.sstatic.net/dEo8p.gif
  [3]: https://oeis.org/A061342
  [4]: https://mathoverflow.net/users/11236/nathaniel-johnston