If something is suffering the death of a thousand cuts, or death by a thousand cuts, lots of small bad things are happening, none of which are fatal in themselves, but which add up to a slow and painful demise.
Someone who by virtue of holding a position of trust with an organization for a long period of time has come to know many of the secrets that others in more powerful positions would rather be kept secret knows where the bodies are buried. An implication is that the person knowing these secrets will use that knowledge to secure something of value for him- or herself.
This is regional southern Midwest American English, and may extend to other areas in the U.S. South. In the phrase, "like to" means "almost," and "died" is hyperbole, expressing the extreme effect on the speaker. Here's an example: "That job was so hard, I like to died".