That is known as the "Sticky-shed syndrome". The deterioration of the tape was caused due to the breakdown in the binder, which sticks the oxide particles on the tape. EMI tape that we used used a non hygroscopic binder unlike the Ampex & Scotch brands used in the US, which used an unstable binder. This is why The Beatles and later Pink Floyd masters are still in pristine condition.Regarding digitising old recordings. I was told in the 90's by people who worked with said tapes that it was a race against time as many tapes from the 60's onewards were beginning to shed - and this is before the Ampex (and others) thing about tapes needing to be baked first before the one safe playing to digitise them...
By the time US and later Japanese manufacturers started manufacturing tape in mass for cassettes they were aware of the issue and stopped using unstable binders. This is why cassette tapes last longer than most master tapes in circulation.