$\textbf{Answer}$

Nothing will happen. The sheep will not be eaten.

$\textbf{Analysis}$

Let's, again, start with simpler situations.

1. If there is just one tiger, then the sheep will be eaten.
2. If there are two tigers, the sheep will not be eaten. This is because whichever tiger eats the sheep, it will become a sheep and then be eaten by the other tiger. Therefore, no tiger will eat the sheep in order to prevent itself from being eaten eventually. This situation can also be analyzed in another way: if one tiger eats the sheep, then there are one tiger and one sheep left. This is the same scenario as the previous case which is unstable.
3. If there are three tigers, the sheep will be eaten. This is because when a tiger eats the sheep and becomes a sheep, the situation becomes the previous case, i.e. two tigers and one sheep, which is safe and stable.
4. If there are four tigers, the sheep will not be eaten. This is because when a tiger eats the sheep and becomes a sheep, the situation becomes the previous situation when the sheep will be eaten

Now, it is clear that the sheep is safe when the number of tigers is even and will be eaten when there are odd number of tigers.

$\textbf{Note}$

From the analysis, we can see that the simplest case of just $1$ tiger is easy to analyze. Then the case of $n \ge 2$ tigers can be derived from the previous case of $(n-1)$ tigers. By this way, we can find the answer for any number of tigers. This method is called induction which is a very important proof method in mathematics.