I think that would be the internal memory, though if you're installing from the USB, I'd guess that trying by removing the USB alone might be a good place to start. If removing the USB doesn't help, maybe try with the HDD, though I'm not sure how difficult removing the HDD is and it might depend...
Is there a specific error code that shows up when the update stops installing?
This seems to be someone updating from the internet rather than USB, but the issue does sound similar and might be of some help since this person was able to get the update to finish with some steps:
Older PS3 stuck...
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