It is NOT uncommon to find bills webbed par their seriel numbers. It isn't ultra common but it is fairly common. What about bills 40 + years old? I have some one's tucked away (two webbed; three, webbed) Anything to this?
The "WEB-Press" notes were very popular while the 1988a, 1993, and 1995 FRN Series were readily available. Even now, some still pop-up. Good luck finding current interest in any but the scarce/rare individuals...
I do believe the OP may be referring not to actual Web notes from the 1990's per se but consecutive notes. Granted, only the OP will be able to clarify and say for sure but I feel this is likely as it would align with the original post quite well.
Would true Webs be worth anything even in circ or heavily circ condition? I pitched a bunch of 88a's I found in straps back into the wild today without checking SNs. They were pretty miserable and looked like someone ran them through the wash with gravel a few hundred times.
Some circulated WEB notes command a premium. Depends on the series, block, and run, and of course, condition. Bob Kvederas authored The Handbook of $1 WEB-Fed Test Notes and the 2nd edition handbook is the latest edition, but published in 2004. You have to research auction archives to get current prices realized.