No, the "emphasizes what comes after" and "emphasizes what comes before" is actually not the case at all. You're misunderstanding.
は is the topic marker.
が is the subject marker.
When they first teach you sentences in Japanese class, they give you は. They say that you use it to mark the subject, and they give you が only in specific pre-constructed grammar forms and never explain why you use it instead. This is technically not true. The reason they tell you this is because trying to teach you the differences between は and が from the beginning would be too confusing, so they teach you something that is technically not grammatically correct, but it's at least understandable.
A: 猫が好きですか？ neko ga suki desu ka?
The subject of this sentence is neko. "Are cats pleasing to you." Cats + が + suki desu ka.
What is the topic of this sentence? Nothing is marked with は here. However even without は、 the topic is implied to be "you". However the "you" isn't actually in the sentence, and so it isn't marked by は。 The subject however is cats, and marked with が。
But what about this response:
B: 母さんは犬が好きですが… kaasan ha inu ga suki desu ga... Well, my mom likes dogs, but...
Here we have a topic change. As for my mother (and not me), she likes cats, but...
The は here is necessary because it shifts the entire focus of the conversation away from Hiroshisan and cats to the mother. It's like emphasizing "Well my mom likes cats, but..."
The subject here is the dogs, which are suki desu. That is, they are likable. The topic is the mom, and we needed は to shift the topic away from the previous lines to this new topic.
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ペンがありますか？ pen ga arimasu ka? Do you have a pen?
The subject here is the pen. Marked with が. The topic is not explicitely marked here, but it's implied to be "you." "(As for you), (do you) have a pen?"
If you answered:
ペンがありません。 pen ga arimasen "I don't have a pen"
The subject here is still the pen. The topic is now implied to be "I", but it's dropped from the sentence because it isn't needed. If the word isn't there, there's no need to flag it with は.
But what about this?
ペンシルはありますが、ペンがありません。 I do have a pencil, but not a pen. Or:
ジョンはペンがありますが、私はペンがありません。 John has a pen, but I don't have a pen.
Here we're changing the topic too. In the first sentence, you're saying "(as for a pencil), I do have that" and changing the topic from pens to pencils. Note that again, the "I" in the second part of the sentence is not needed and so it isn't there, or marked. However the topic of the conversation is shifted from pens to pencils. "As for a pencil (but probably not a pen), I do have that."
Note that in the first part of the sentence, we've changed the subject as well. Both the subject and the topic are temporarily pencils, however the topic particle always takes precedence over the subject particle if both are valid.
In the second sentence, we change the topic twice. "John has a pen but..." changing the topic to John, because you're trying to say John has a pen but you don't. Then you have to change the topic back: "but (as for me, I) don't have a pen," changing the topic back to you. The subject, however, has remained unchanged this entire time: pens.
Do you see how that works? が simply marks the subjects of the sentence. は actually shifts the entire topic of conversation to a new topic temporarily.
When you first learned:
私は（名前）です。 "my name is _____" they taught you to use は. Why did they do this? What you're actually saying is changing the topic to yourself. "As for myself, my name is _____" or "My name is _____." You're actually doing a full topic change, not simply marking a subject. But they don't teach you this, because when you're first trying to put together simple sentences, trying to teach you the differences between は and が would be so confusing, you couldn't even manage to say your name without getting confused.
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However to make matters even more confusing, native speakers will often drop the は or が.
For instance in our first example, if I said:
博さん、猫が好きですか？ Hiroshisan, neko ga suki desu ka? The topic is Hiroshisan. Why isn't it marked with は？ The truth is that it could and probably should be, but simply saying someone's name, pausing slightly, then asking the question is actually more natural sounding that a full 博さんは猫が好きですか.
So here we've dropped the は topic marker, but it's clear from context where it should be, and what the topic is. But looking at that sentence, you would probably be kind of confused about what's the topic and what's the subject. Native speakers, however, know what those parts are without them even really needing to be explicitely marked. They imply it through pauses, or just by sentence structure. That's why a lot of times as a Japanese learner, you'll get confused. The particles are still there, and are still technically necessary -- they're simply just not said instead.
