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Two poles on 0 and -1 and no zeros. This is the case for open loop. But when I close the loop with unity feedback and add a K gain, I end up with following transfer function;

K/s^2 + s + K

So, clearly the poles are now at somewhere else. However, for example in this video, poles are still considered where they were with open loop;

I am very confused with this. For a closed loop system, do I have to change the poles according to second transfer function. Likewise, adding a lead compensator, something like (s+a)/(s+b) would change the transfer function with a unity feedback and the denominator of the lead compensator, which is (s+b) would appear in the denominator of the new transfer function after closing the loop with unity feedback.

But in the same video he just puts the poles and zeros coming from the compensator.

Appreciate if someone can clarify this.