Not a Stevens buff by any means, but I thumbed through my Gun Trader's Guide and here is what I found.
There is no 404, but there is a model 44 that is a rolling block single shot.
Model 44 is described as such for the .22 variant:
Rolling Block, lever action takedown. Bbl lengths, 24' and 26' (round, half octagon, full octagon). Weight: 7lns w/26' round bbl. Sights: open rear;Rocky Mountain front. Plain staight grip stock and forearm. Made 1894-1932.
There is a 44.5, falling block and is described as follows:
Falling block. Lever action rifle. Aside from the new design action intro. 1903, specifications of this model are the same as thoseof model 44. Model 44X disc. 1916.
The prices for these are:
Model 44 Ideal single shot: New in Box $744, Ex $595, Good $405
Model 44.5 Ideal Single shot: NiB $938, Ex $750, Gd $510
Hope that helps a little bit.
SAWgunner