The story
Thumb looks like lamb and comb, but its history runs the other way. Old English þūma had no B at all — German Daumen and Dutch duim don't have one either. The word probably goes back to a root meaning "to swell" — compare Latin tumēre.
The B started appearing in spellings in the late 1200s. It is what linguists call a parasitic or excrescent letter: after words like lamb and comb had lost their final B in speech, writers had a pattern — "-mb" spelled, "-m" said — and they extended it to words that had only ever had an M. Crumb and limb got the same treatment.
So the B in thumb is silent not because people stopped saying it, but because no one ever did. It is a spelling fashion that stuck — the same kind of thing that happened, centuries later and for different reasons, to the B in debt and doubt.