No, everyone takes care

Everyone has to take care for him(her)self in US. Only a child has to be token cared by his parrent.

If her status is legal or illegal has nothing to do with you or any impact to you.

But as a nice hu*****and, if she is dependent on you, you may warn her when her status will become a problem.

If you extended H-1, her H-4 can be extended by herself by marriage.

If you filed I-485. she can file I-485 herself with the marriage centificate. Even without your notice at all.
No any signature from you is required. No I-134 is required as someone said.

You can chose to do nothing if you want to. It is your privacy.

If you want to help her, that's different.