What are the value of the pixels of the convolved image? I'm studying convolutional neural networks from the following article https://ujjwalkarn.me/2016/08/11/intuitive-explanation-convnets/.

If we take a grayscale image, the value of the pixel will be between 0 and 255. Now, if we apply a filter to our "new image", can we have pixels whose values are not included in this range? In this case, how can we create the convolved image?
The convolved image can be considered a feature map, where each new neuron represents some indication (or lack-there-of) of a feature in some receptive field of the original image, so no it does not need to be a valid image in the output.  

If you specifically care for it to be an image as an output, you can do a couple of things:  

1) normalize the produced feature map to some set range that youre working in (0-255 or 0-1)  

2) make the filter a valid probability distribution, and you know the output will stay in the same range as the input (ex: Gaussian filters)