Probably the most well-known manufacturer of composition figures was Elastolin, so much so that its brand name has become synonymous with 'sawdust composition.' Figures produced by Lineol, Neo-Form, Danolin, and many other companies are often labelled as "Elastolin" on the second-hand market. At the moment I rely on Animalkings Figurenshop for identifying brands/manufacturers, but I'm unsure exactly how reliable that website is.
Composition recipes often included too much moisture, which caused the figure to develop cracks as they dried. It is very rare to find sawdust composition figures without cracks, especially in the legs.
Some sawdust composition figures grow more brittle with age, and will shatter like glass when dropped. Even when handled with care, they may develop stress cracks from temperature/humidity changes.
Do not under any circumstances get sawdust composition figures wet. Dust them off with a brush. If they require cleaning (as second-hand figures often do, having been produced during a time where everyone smoked indoors, and sooty grime covered every surface), do it with a moist (not wet!) cotton swab and proceed with extreme care. Do not under any circumstances store composition figures near windows, bright lights, or heat sources.