It can be negative, because these parameters are then used to describe the transformations that are needed in order to convert one reference frame to another. For example:

So if we want to go from frame $i-1$ to frame $i$ we have to do the following:
- a rotation about $x_{i-1}$ for $a_{i-1}$ in order to make the $z$ axis parallel
- a transport in $x_{i-1}$ axis for $r_{i-1}$ in order to go to the $z_i$ axis
- a rotation about $z_i$ for $θ_{i}$ in order to make the $x$ axis parallel
- a transport in $z_{i}$ axis for $d_i$ in order to reach the origin of the $i$-th frame
Because all the transformations were done in relative frames, we multiply the homogenous transformations from the right.
So the transformation matrix is:
$$ T_i^{i-1} = Rot_x(a_{i-1}) Trans(r_{i-1}) Rot_z( θ_i) Trans (d_i) $$
So the sign of the parameters are important.
Also, another way to see it is how we use them in the Transformation Matrix:
$$ T = \begin{bmatrix} R_i^{i-1} & b^{i-1} \\ 0 & 1 \end{bmatrix}$$
where $b^{i-1}$ is the vector in the $i-1$ frame that points to the origin of $i$. This vector is given (at least in the convention i use, taken from craig's book pg.83):
$$b^{i-1} = [r_{i-1} \ -sin(a_{i-1})d_i \ cos(a_{i-1})d_i]^T$$
For this vector, the sign of d_i is important. In the convention used by craig, you take the signed distance from $x_{i-1}$ to $x_i$.