The 'sign' pictures are an attempt to verify that the woman writing the romance scam letters, is the same person in the pictures they send. Usually they are digitally edited to change the name on the sign, for each new victim, change the face of the lady holding the sign, or add a sign to a picture that didn't have one! They are RARELY 'real' and unedited!
The 'sign' pictures are sometimes sent at the request of the victim, but also may be sent without asking by the scammer, in an effort to prove they are 'real', or in 'love'.
To me, they're an interesting trophy, and not much else. If you do get an unedited 'sign' photo, it is safe to assume that the woman in the picture is involved in scamming.
More 'sign' pictures from my collection at: http://russianromancescammers.forumup.org/about95-russianromancescammers.html