When should we use an adjective instead of an adverb after verbs(main verb)?

Strong wind, sweeping almost unchecked over great distances, is a prime component of the grassland climate.

If you change the above sentence to

Strong wind sweeps unchecked over great distances

it is easier to understand.

"unchecked" complements the subject wind at the time it sweeps. That's why it could be called either "predicative-complement" or "quasi-complement". The sentence could be rephrased to

Strong wind sweeps over great distances and it is unchecked.

The more obvious examples are as follows;

She came home happy. = She came home and she was happy.

Happy complements the subject when she came home. That's why you don't use "happily".

He died young. = He died and he was young = He died young when he was young.