Learn Swedish: Han arbetade hårt för att aldrig bli en börda. - He worked hard to never become a burden.

Because this is an infinitive phrase. When you use att followed by a verb in the infinitive form (like bli), sentence adverbs such as aldrig (never) or inte (not) must be placed right between att and the verb. This is why it is att aldrig bli.

Would the word order change if this was a normal main clause instead of an infinitive phrase?

Yes! In a standard main clause, the verb must come in the second position (the V2 rule), so the adverb usually comes after it. For example, if you just wanted to say He never becomes a burden, it would be Han blir aldrig en börda.

Why do we need för att here instead of just att?

The phrase för att specifically means in order to and expresses the purpose behind an action. He worked hard in order to never become a burden. If you only used att, it would sound grammatically incorrect in Swedish because att alone cannot express purpose.

Why does the word hårt end in a -t?