In modern terminology, a digital signature scheme with a shadow is a (digital) signature scheme giving (total) message recovery. The shadow is the message representative.
The paper linked in the question refers to it's reference [12] for the definition of shadow. That's Louis C. Guillou, Marc Davio & Jean-Jacques Quisquater's Public-Key Techniques: Randomness and Redundancy, in Cryptologia Volume 13, 1989 - Issue 2, p.167-189.
Reading this, the term shadow is used for a message representative in an e.g. RSA-based signature scheme. That shadows embeds a relatively small message with added redundancy, and is passed to e.g. the textbook RSA private key function to obtain a signature giving total message recovery, in the modern terminology of ISO/IEC 9796-2:2010.
An example of that is ISO/IEC 9796:1991, which signature embeds a message up to about half of the signature size. That message is returned as a byproduct of signature verification. The scheme is withdrawn because it's EUF-CMA security is broken with 1 or 3 chosen-message queries, due to the rather ad-hoc way the message representative (shadow) is built. An equivalent INCITS standard still seems purchasable.
A free online source explaining ISO/IEC 9796:1991 is section 11.3.5 in the HAC. The shadow would be $\mathsf{MR}$ there.
A modern equivalent with a security reduction would be ISO/IEC 9796-2:2010 scheme 3, which signs with a lower size overhead of $2b+16$ bits for $b$-bit security, or Louis Granboulan's OPSSR which further lowers overhead / increases the amount of message embedded in the signature.
Note: EMV 4.4 Book 2 describes ISO/IEC 9796-2:1997, simplified by a restriction to byte-aligned messages and keys. This scheme remains in the 2010 edition (with some tweaks), although it's EUF-CMA security is broken with some thousands chosen-message queries. This and ISO/IEC 9796:1991 are still in use, and that does not lead to fraud, because existential forgery under chosen message attack is only an issue in some applications.
