When I was researching the mess related to strange and poorly documented CPUID bits in the Athlon MP and XP processors, I had to swap a lot of CPUs. This was uneventful in most cases… but only most.
When I removed the heatsink from one unlucky Athlon XP, the processor looked like this:

And this is what the heatsink looked like, with a piece of the CPU glued to it:

There are two interesting things about this. One is that the CPU worked just fine until a good chunk of it came off. The other is that removing the heatsink did not need any particularly excessive force, although some heatsinks do have a tendency to get stuck on.
Based on the shape of the “extracted” piece of silicon, I suspect there was a relatively long and straight micro-crack in the silicon which did not noticeably impact the operation. But when force was applied, the micro-crack gave way, and then a whole big chunk of silicon came off.

Notice how the right-hand side of the gouge in the CPU is very straight, whereas the left-hand side shows typical fracture marks.
It is notable that around 2000, both Intel and AMD used flip-chip PGA packaging in an effort to provide better cooling (something both companies struggled with as the TDP of the processors quickly shot past 50W and approached 70-80W).
Both companies, especially Intel, gave up on this type of packaging relatively quickly. Intel only used it for some PIII models and switched to lidded CPUs for the P4 line, as well as the PIII-S processors. AMD used flip-chip packaging for PGA Athlons but not for Opterons.
The exposed silicon was a little bit too fragile and required assemblers to install heatsinks very very carefully—if installing a heatsink applied pressure that was too uneven, the silicon would crack. Many vintage flip-chip CPUs have chipped corners, although that usually does not affect operation.
Processors with lidded packaging still provided very good cooling, but compared to CPUs with exposed silicon they proved much sturdier and far less susceptible to mechanical damage. Especially Intel’s pin-less LGA processors are quite sturdy and not at all prone to mechanical damage, although the weak spot simply moved to the motherboard socket instead.