- [to be] better off or worse off
is an idiomatic expression or idiom.
Idioms often function in peculiar ways that have their own logic. Native speakers know how to use them instinctively (they are learned by being heard when used by other native speakers as one grows up, etc.)
Better off (or worse off) can be followed by clauses introduced by now that, after x, or if x or a gerund or gerund phrase or prepositional phrases or just an adjective.
Let's take a look at these examples from the Collins Dictionary:
better off in CD
be better off
- to have more money than you had in the past or more money than most other people:
- Obviously we're better off now that we're both working.
- When his parents died, he found himself $100,000 better off (= he had $100,000 more than before). [adjective]
- to be in a better situation, if or after something happens:
- He'd be better off working for a bigger company.
- implies if = He'd be better off if he were working for a bigger company.
That said, we can turn the sentence another way.
- Working for a bigger company, he is now better off.
- Working for a bigger company is a good thing.
working for a bigger company = a gerund phrase.
But even: "He is better off working" or He is worse off not working", are gerunds.
"He's better off at home". is a prepositional phrase.
"She's better off rich". is an adjective.
[I think I covered most of these idioms' peculiarities alluded to above. The point for a learner is to internalize examples so as to be able to refer to them in the future. ]
Non-gerund nouns cannot come after "to be better" or "to be worse off":
For example, "You'd be better off a bird" is not grammatical and would be said: You'd be better off as a bird. I suspect that this is because better off follows the comparative rule for better: "You'd be better as a bird".