Ryan Taylor, 30, who was serving a 55-month sentence, was found in his cell at Featherstone Prison in April.
His grandmother Susan Palmer said the family was told by prison staff he had had a heart attack, but they want a full inquiry.
The Prison Service said police were investigating.
Mrs Palmer, 81, of Stoke-on-Trent, said they had heard "rumours" Ryan had been attacked by other inmates and also had glue put in his mouth.
She said her daughter, Ryan's mother, was not told he was in hospital until five days after the incident on 29 April. He spent three weeks in intensive care.
"Ryan was a healthy, strapping lad before he went in, so it is hard to believe he had a heart attack," she said.
Mrs Palmer fears he will never recover and said family members were "devastated".
"He is not in a coma, but he might as well be. He can't talk, he can't move and is just blinking," she said.
Taylor, of Berryhill, Stoke, had served 15 months of his sentence for burglary, false imprisonment, wounding and affray.
The Prison Service said: "The police are investigating this incident, so it would be inappropriate to comment further at this stage."
It added: "The justice secretary has been clear that safety in prisons is fundamental to the proper functioning of our justice system and a vital part of our reform plans.
"There are a number of factors that need to be tackled. We are determined to make sure our prisons are safe and places of rehabilitation."
Staffordshire Police said officers were investigating the circumstances of Ryan's collapse after the case had been referred to them by Featherstone and they "were working with the prison to understand the facts".
The family of an inmate who is unable to walk or talk five months after being found collapsed in his cell has called for "answers" to what happened to him.