grammaticality - Instilling a sense of something

I do not get the meaning of the bold text in the following sentence:

One broken window, left unrepaired for any substantial length of time,
instills in the inhabitants of the building a sense of abandonment—a
sense that the powers that be don’t care about the building.

I could find two entries in the dictionary regarding having a sense of something:

• If you have a sense that something is the case, you think that it
  is the case, although you may not have firm, clear evidence for this
  belief.


• have a sense that/get a sense that
  Do you have the sense that you are loved by the public?

But the above sentence I quoted is unlike the dictionary examples and does not make any sense to me. If it was something like "a sense of being don't care about the building", that would have some meaning to me. If it is grammatically correct, please somebody explain it to me.

• Next lord of the rings - In canon, why is Saruman so focused on Frodo?
• Previous meaning - Appropriate word for smile