Common issue on some older chips. The thermal paste gets really thick when cool and the CPU comes out of the socket still attached to the heatsink.
This came out of an HP DC5000 computer. We had someone that complained their DC5000 was running really loud all the time. One of the guys pulled the heatsink off on this noisy PC to clean off the old compound and replace it with some Arctic Ceramique I have. However, he stopped there and left the office for a while.
I came into his office, saw what he was up to and thought I'd help him out. I cleaned it up and applied the new compound, then went about seating the heatsink. I put one of the clips on, but saw that the second clip had a loop broken off the plastic mounting bracket (it's a S478 Pentium 4 CPU). We had another DC5000 that that had it's own issues, so I planned on taking the bracket off that one to use on the noisy PC. I undid the clips on it and removed the heatsink, only to find the CPU stuck to the bottom of it (and of course, the nasty dust, dander, wtf mess underneath).
If this was one of my computers for home, I probably would have warmed the CPU up a little before I unmounted the heatsink.