I illustrated a book 20 years ago. No royalties: one-time use. Did not sign a contract for copyright. It is considered an orphan. Now the author wants a new publisher to print the same illustrations. Do I have any rights? I do not have the contract. The publisher is out of business and I may not even have the originals any more.
You need to consult with a lawyer. This question overlaps with contract law and copyright law and seeing as you don't have any of the original contracts it will be difficult to establish what happened. Presumably, however, the author of the book has also lost whatever agreements were in place, or they could provide copies for you?
I'm going to assume you're posting from a country that follows the Berne convention on copyright. In those countries, any work you create is automatically copyrighted. The length of the term of copyright varies but it's usually much longer than 20 years. You may have difficulty establishing proof that you are, in fact, the illustrator, but maybe you can get the author to stipulate that? If so, then the works would normally automatically be copyright by you.
When dealing with a publisher, it's common for the copyright to be transferred, either as a work-for-hire or outright sold or otherwise locked up. In this case you'd have no remaining interest in the works and would be out of luck. A "one time job with no royalties" sounds like a "work for hire", but without a formal agreement it's difficult to say. If you can establish that there was no transfer of copyright, then the works are yours and you should be party to the negotiations for the new publishing.
Illustrators are often paid a fraction of the royalties. A common split is 50-50: the author gets half the royalties, the illustrator the other half. A big-selling author or illustrator may be able to get a larger cut. It's all about negotiation.
Were I in your position I'd first try to determine what the author intends with regards to royalties. The fairest option is to split the royalties. Maybe they will do that for you? If not, maybe they can provide evidence that the illustrations were contractually a work-for-hire? If the author is not cooperating with you, you should probably get a copyright lawyer to review your case. Maybe sending the author a single letter from the lawyer will outline your rights and convince them to give you royalties. If the author is shopping the book out to traditional publishers you will probably need to negotiate with the publisher directly.
Finally one thing to consider is that the book may not be an orphan after all. If the original publisher held copyright on it, its interests may have been purchased by some other organization. That could pose a problem for you. Again, a lawyer should be able to help you with that.