If the initial state of Conway's game of life is a line of $n \in [0,100]$ alive cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.
Question: Is such a line non-vanishing for any $n \in [25,\infty)$?
Edit
Definition: a finite pattern $p$ has a weak period $wp$ if for any cell $c$ in the grid, there is $k>0$ such that the set of cells which are neighbours of neighbours of neighbours… ($k$ times) of $c$, is periodic of period $wp$ after sufficiently many generations, from the initial state $p$.
The sequence A061342 gives the weak period $wp_n$ of a line of $n$ alive cells. By combining the checking above with the fact that $wp_n \ge 2$ for $n \in [84,1000]$, we deduce that the pattern is non-vanishing for $n \in [25,1000]$. We observe that for $n=500$, four gliders are produced on the boundaries after $435$ steps, but $435<500$, so this must happens $\forall n \ge 500$. Assuming that these gliders (or others) are perpetual (as stated implicitly by Nathaniel Johnston in A061342, although without reference, while the proof could be non-trivial, as pointed out by Will Sawin in the comments), the answer to the above question would be yes.
Definition: a finite pattern $p$ is weakly-vanishing if any cell $c$ in the grid becomes perpetually dead after sufficiently many generations (depending on $c$), from the initial state $p$.
Improved question: Is there a weakly-vanishing line of $n$ alive cells with $n \in [25,\infty)$?
Stronger question: Is $wp_n \ge 2$ for any $[84,\infty)$ ?
Tobias Fritz pointed out in the comments that there is a one-cell thick pattern with infinite growth (see this page), but it is disconnected. Bonus question: Can that happen in the connected case?
Best Answer
Just to help develop intuition - here is a fragment of a typical evolution for large $n$ (made with Golly)