After Negan dispatched Glenn and Abraham on The Walking Dead, he dragged Daryl off as a prisoner — and being a prisoner of Negan's is as awful as one would expect it to be. Daryl spent the first half of the appropriately named episode, "The Cell," locked up in Negan's compound, the Sanctuary, while his morale slowly began to erode day by day. He was kept in filthy conditions, at first without clothes, and forced to chow down on dog food sandwiches, while irritatingly cheery music played on repeat in the background. At a certain point, however, it became clear that Daryl would have a choice to make: he could continue to suffer, or he could choose to join forces with Negan. Will Daryl become a Savior on The Walking Dead?
The choice is presented to him by Dwight, who doesn't seem too thrilled to be amongst Negan's people himself anymore. He showed Daryl the walkers who line the outer parts of the Sanctuary and the people who have to deal with them, presumably as punishment. Dwight informed Daryl that he can be like those people, or he can be like Dwight. Other citizens of the compound assured Daryl that Negan will take care of him, insisting that it's better to comply than to try and fight. But Daryl isn't so willing to give in, at least not at first.
As soon as Daryl was given an opportunity to escape, he took it, despite the fact that other Saviors in the compound warned him not to. It's the first sign that Daryl isn't totally beaten down by his imprisonment, that he might still have some fight left in him. Sadly, he doesn't end up getting very far before being overtaken by the Saviors and Negan himself. But Daryl doesn't so much as flinch during the altercation. Apparently this was an appealing quality for Negan; he seems to like that Daryl doesn't scare easily.
Negan went on to make his offer fairly clear. He wants Daryl to be a Savior and a high ranking one at that — someone he can truly count on. But to do that, Daryl has to give up everything about himself, even his own name. Negan's people offer him complete fealty, bending the knee when he walks by and answering with Negan's name when asked who they are. They give up their identities for Negan, and he uses that as a little test for Daryl, to see how willing he is to join forces. But when asked who he is at the end of the episode, Daryl still responded with his own name. Thankfully, he's not willing to give up just yet.
Later, when Dwight throws Daryl back into his cell, Daryl told him that he understands the sacrifices Dwight has made for those he cares about, but the reason Dwight gave in to Negan is the same reason why Daryl can't. He has people out there who he loves and he has to stay strong for them. Even seeing that Polaroid of Glenn after his death wasn't enough to break him, though it came close. But who knows how long poor Daryl can be expected to hold out if Negan's torturous methods continue. He hasn't given in yet, but it's clear that he has a difficult journey ahead.