Find the largest number that's adjacent to a zero

MATL, 10 bytes

t~5BZ+g)X>

Try it online! Or verify all test cases.

Explanation

Let's take input [-4 -6 -2 0 -9] as an example.

t     % Input array. Duplicate
      %   STACK: [-4 -6 -2 0 -9],  [-4 -6 -2 0 -9]
~     % Logical negate. Replaces zeros by logical 1, and nonzeros by logical 0
      %   STACK: [-4 -6 -2 0 -9],  [0 0 0 1 0]
5B    % Push logical array [1 0 1] (5 in binary)
      %   STACK: [-4 -6 -2 0 -9], [0 0 0 1 0], [1 0 1]
Z+    % Convolution, maintaining size. Gives nonzero (1 or 2) for neighbours of
      % zeros in the original array, and zero for the rest
      %   STACK: [-4 -6 -2 0 -9], [0 0 1 0 1]
g     % Convert to logical
      %   STACK: [-4 -6 -2 0 -9], [0 0 1 0 1]
)     % Use as index into original array
      %   STACK: [-2 -9]
X>    % Maximum of array.
      %   STACK: -2
      % Implicitly display

05AB1E, 9 bytes

ü‚D€P_ÏOZ

Explanation

ü‚         # pair up elements
  D        # duplicate
   €P      # product of each pair (0 if the pair contains a 0)
     _     # logical negate, turns 0 into 1 and everything else to 0
      Ï    # keep only the pairs containing at least 1 zero
       O   # sum the pairs
        Z  # take max

Doesn't work in the online interpreter, but works offline.

Haskell, 63 43 bytes

f x=maximum[a+b|(a,b)<-tail>>=zip$x,a*b==0]

Thanks to @MartinEnder for 4 bytes!