Is this sentence correct?

Is this sentence correct?
Hello everyone,
As I know we can use an adverb to modify a prior verb. But why the following sentence did not use an advaerb but an adjective instead?
I heard a noise and woke up rigid with terror.

Let me ask one more question. When do we use an adjective to modify the preceding verb?
She feigned sleep, lying rigid in bed.
I feel okay with this sentence, though I know ‘rigid’ has an adverb form which is ‘rigidly’.
Thanks.

This is a reasonably common pattern in English. The adjective describes the state of the subject during, immediately after, or as a consequence of the action described by the verb.

“I sat motionless”
“He arrived home safe”
“She dropped dead”
“I left dejected”

However, you can only use this pattern with certain verbs, and certain verb-adjective combinations. If you start combining verbs and adjectives arbitrarily then you will end up with nonsense.

There seems to be a blurry line (if any line) between these usages and so-called “copula® verbs”, such as those listed at usingenglish.com/glossary/copula-verb.html . I am not very certain of the terminology in this area.

They are described on TOEFL test more widely at Cliff’s suggestion book, few at Barron’s.

Do you happen to recall what name (if any) these sources give to this type of construction?

Adjectives with linking (copulative)verbs.

like

feel,look,smell,taste, appear, seem, sound, be, become, remain, and stay etc.

They don’t show action, so they are modified by adjective no adverb.e.g.

I feel bad(instead badly)about my test grade.

There are also more rules here. Generally we should avoid unauthenticated sites or qualified people don’t suggest as a lot of English or other sites may mislead you, Because, it is depend on the site administrator’s own merit as you may not feel your some classmates are good in one particular subject, just as like this.