In Chapter Seven of Stranger Things 4, the Friendly Orderly character shows Eleven a small implanted device in his neck, just under the skin. El rips the item out with her telekinesis. Since this was such simple surgery, why didn't Friendly Orderly do it himself with a knife or another instrument? It would be painful, but not any more so than what El did. And as we see later in the episode, it was extremely important to him to have it out.
The only somewhat plausible explanation would be that it was very important to him to win over Eleven as an ally. He kept back and made it look like he was relying on her. Her removing the device started to look like a stepping stone in them bonding.
I'll concede that still leaves a window where the Friendly Orderly should have been able and motivated to remove the device. So far we can only speculate. Maybe he was formerly far more heavily restrained and the device and his working as Orderly only came when Eleven was already there, at which point he decided that he wanted here as an ally.
Edit: TV Tropes has two theories that are very relevant (yet not perfect): Either the Friendly Orderly is Eleven's father. Then he would have waited long enough for her to be somewhat self-sufficient to take her with him (but then why not leave a few years earlier?). The other is that he is grooming her to have children with her (but then why not wait a little longer?). In both cases her beating Two could have been the signal for the Friendly Orderly to leave.
This very implant was not only used for tracking him but also to make him weak. He cannot use his powers due to that. It is called Soteria, who is a goddess of safety and salvation, deliverance, and preservation from harm in Greek mythology. It explains why he is weak and cannot use his powers. This is why he couldn't remove the implant.
Friendly Orderly: Here. Can you feel it? Your papa calls it Soteria. It weakens me. It tracks me.
From an article by Bustle(emphasis mine),
After Eleven slipped another orderly on the way to the infirmary, the pair rendezvoused and One explained the limitations of his powers. He explained that Brenner had implanted something called Soteria in his neck. “It weakens me. It tracks me.” (Interestingly enough, Soteria is also the Greek goddess of safety, and deliverance and preservation from harm.) Because he’d helped her, Eleven then restored One’s powers by using her own abilities to telekinetically remove the implant from his neck.
So, when Eleven removes it, he gets his power restored which he unleashes on the guards and almost everyone in the Hawkins lab. From the same article,
No longer inhibited, One unleashed his powers on the guards before revealing his 001 wrist tattoo to Eleven.
Much of this season didn't make sense, but here's my explanation...
Nobody had any idea how 1's powers worked, and they were entirely mental in nature. So the implant didn't (couldn't) suppress them by some sort of magical physics that prevents Powers. Instead, it is the interface to some sort of brain implant set to scramble mental functions whenever the pattern of activity looks "unusual". It would be a little like a lie detector, if you believe in lie detectors. If its design worked perfectly, any time our hero would think of using his powers, fondling spiders, or trying to escape himself, it would have some way to scramble and reset his thinking. But his exhortation to 11 to use her powers was pretty much like his ordinary work in the lab, so it didn't flag it and reset his thoughts.