Regex optional capturing group?

The reason that you do not get an optional cat after a reluctantly-qualified .+? is that it is both optional and non-anchored: the engine is not forced to make that match, because it can legally treat the cat as the “tail” of the .+? sequence.

If you anchor the cat at the end of the string, i.e. use ^(dog).+?(cat)?$, you would get a match, though:

Pattern p = Pattern.compile("^(dog).+?(cat)?$");
for (String s : new String[] {"dog, cat", "dog, dog, cat", "dog, dog, dog"}) {
    Matcher m = p.matcher(s);
    if (m.find()) {
        System.out.println(m.group(1)+" "+m.group(2));
    }
}

This prints (demo 1)

dog cat
dog cat
dog null

Do you happen to know how to deal with it in case there’s something after cat?

You can deal with it by constructing a trickier expression that matches anything except cat, like this:

^(dog)(?:[^c]|c[^a]|ca[^t])+(cat)?

Now the cat could happen anywhere in the string without an anchor (demo 2).