All of the words you provide (limb, thumb, crumb) are listed in my local dictionary without a
b sound. Things seem basically the same with suffixes (i.e. thumbed has no
Crumbled is is a completely different word and receives the pronunciation typical for "mble": thimble, tremble, fumble, etc.
It is true that crumb and crumble have common origins:
crumb - O.E. cruma "crumb, fragment," from a W.Gmc. root of obscure origin (cf. M.Du. crume, Du. kruim, Ger. krume).
crumble - late 15c., kremelen, from O.E. _*crymelan_, presumed frequentative of gecrymman "to break into crumbs," from cruma (see crumb).
The "b" in each word appeared later (mid-15c for crumb and 16c for crumble). Given the typical pronunciation of the "mb" and "mble" it isn't surprising that these words are treated the same. Why they received a "b" at all is a little vague from the notes in the above link.
Digging deeper I found Anatoly Liberman who gave a more thorough explanation:
The words thumb, numb, and dumb have unetymological mb in spelling, though they do not end in l. Why do they? In principle, the story begins in late Middle English. At that time, consonantal groups were often simplified. Solemn and column are now pronounced without n. In the speech of some people kiln is homophonous with kill, g is always mute in diaphragm, phlegm, and so forth. Because of the simplification, lamb was fleeced of its historical final b; today b is retained in spelling but not in pronunciation. The same happened to jamb, plumb, and tomb (borrowed words), along with womb (Old Engl. wamba “belly”; compare Wamba, the name of Cedric’s “fool” in Ivanhoe) and climb (Old Engl. climban).
As long as the simplification of consonantal groups remained an active force, literate people felt uncertain when to write m, as opposed to mb, and began to add b to m gratuitously, a mistake (here, reverse spelling) called hypercorrection. This accounts for the modern forms limb and crumb.
The rest of that article is extremely fascinating and highly recommended. Also relevant are words like limber, timber, combine which most certainly pronounce the
b despite the "mb". So are other cases of a silent "b": debt, subtle, etc.