Dafydd and a few companions had no food or shelter, and had to stay on the run from English soldiers. On 22 June he was captured along with one of his sons, Owain ap Dafydd. (Owain and a brother who was captured later would remain in captivity for the rest of their lives, even being locked into a cage at night so there was no chance of escape.)
Dafydd was taken to the encampment of Edward, who summoned Parliament to Shrewsbury to determine the traitor's fate. He was convicted of High Treason against his king—the first time such a verdict had been brought in England. His punishment needed to be significant to match the crime. On 3 October the sentence was carried out. Let me quote myself from 2013:
He was tied to a horse's tail and dragged through the streets to the place where he was hanged. His body was cut down before death was certain; he was revived, then he was cut open and his entrails pulled out and set afire so that he could see it all happening. His body was then cut into 4 pieces, the parts going to different parts of the kingdom to be put on display. The person given the task of seeing all this done, Geoffrey of Shrewsbury, was paid 20 shillings for the job.
Part of the viciousness of the punishment was because of the sacrilege that Dafydd committed by starting his rebellion on Palm Sunday, desecrating Holy Week.
His daughter and Llywelyn's infant daughter were sent to convents in Sixhills and Sempringham, respectively. There were a few relatives that survived capture, who actually tried rebelling years later, but Wales was now under English rule, and therefore was going to be subject to English rules. Tomorrow we'll see the attempt to replace the Laws of Hywel Dda with the Statute of Rhuddlan.