This answer will be given to the second part of the OP question, specifically for the English native speakers, as opposite to the languages Latin, Russian, etc., with Declension and Conjugation including all forms of the reflexive and personal pronoun (let's call it the DC-language). This is the standard and often repeating confusion regards of the question "why is no subject-pronoun used in that sentence?"
There is not always the case when two subjects does correspond to given two pronouns and one verb.
Quick Example 1:
And... um... he, he was standing there.
Have we two subjects for given verb "be" there, or have we none? Have we any subject at all? Yes, we have. Is it the first or second one? If the second pronoun is the subject, what is the precise role and functions of the remaining one?
In the DC-language, there is no grammatical need for a related subject pronoun, if a form of a given verb has such grammatical properties reflected in the morphology of the verb, that it unambiguously pointed out at the unique pronoun. Hence the two examples were given by me:
"Подели небо поровну", instead of
"Ты подели небо поровну". The pronoun "Ты" is completely unnecessary, from the grammatically point of view.
Quick Example 2:
I am not going to give myself up.
In the DC-language, "where is it" and "who is the subject", what tense, perfectiveness, and other grammatical values can be packed tightly, fulfilled, literally, in one word. So, in the DC-language, when reader has received this information expressed in an extra word, this word is to become for him the amplification particle. In English, it is "um... he, ..." from the example 1. As a vivid example in Russian, look at the phrase "да нет", where 'да' is not 'yes' but an unstressed particle emphasizing 'нет'. What a meaning speaker is amplifying, depends on the context.
"Я не дамся" is emphasizing, in the DC-language, that it is namely Me, not You.
"Ты подели небо" give us the same additional point, namely You, not Me.
There is nothing specifically related to the lyrics domain. It's everyday usage.