Find arsonist's lullaby
MATL, 32 bytes
JQ6*`G5thYay&amp;Zj3$)wyJ2@-^*+8M]b&amp;

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How it works
The input matrix is padded with a frame of five zeros, so for example
3 2 3 2 7
3 1 4 1 6
2 5 3 1 1
4 4 3 2 4
1 1 1 1 1

becomes
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 3 2 3 2 7 0 0 0 0 0
0 0 0 0 0 3 1 4 1 6 0 0 0 0 0
0 0 0 0 0 2 5 3 1 1 0 0 0 0 0
0 0 0 0 0 4 4 3 2 4 0 0 0 0 0
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

The frame of zeros is used to detect when the arsonist bee has exited the matrix. The extension with five zeros ensures that a modular displacement of length up to 9 in any direction from any of the nonzero entries will correctly land in a zero without wrapping around to some non-zero entry.
In matrix coordinates, the bee starts at entry (6,6) of the extended matrix. It reads that entry, and updates the coordinates as required, applying a (modular) displacement of the read length in the corresponding direction. This is repeated in a loop until the read value is 0. The entry that was read before that one (i.e. the last non-zero entry) is the output.
The coordinates are actually stored as a complex number, so for example (6,6) becomes 6+6j. This way the four cyclic directions can be realized as powers of the imaginary unit. The corresponding power (j, 1, -j or -1) is multiplied by the read entry to obtain the complex displacement which is used for updating the coordinates.
The successively read values are kept on the stack. When the loop is exited, the stack contains all non-zero read values in order, then the last read value which is 0, then the latest complex coordinates. So the third-top element is the required output.